Hi

I

A TREATISE ON HEAT.

TREATISE ON HEAT

PART I,

THE THERMOMETER; DILATATION; CHANGE OF STATE: AND LAWS
OF VAPOURS.

BY THE

REV. ROBERT V. DIXON, A.M.,

FF.LLOW AXD T1TOR. TRINITY ' < >M.I-.'.K. TTl'.I.IV ; AM- F.KASVrS SMITH'S rROFRSSOR OP NA1

i-iiii.' — TIIV.

DI BL1 N:

HODGES AM) SMITH, <;ii.\KTON-STKI

MI •

DUBLIN :

PRINTED AT THE UNIVERSITY PRESS,
BY M. H. GILL.

TO 'THE

REV. HUMPHREY LLOYD, D.D., S.F.T.C.D.,

PRESIDENT OF THE ROYAL IRISH ACADEMY,

FORMERLY PROFE88OR OF NATURAL AND EXPERIMENTAL PHILOSOPHY IN THE
UNIVERSITY OF DUBLIN,

THE FOLLOWING PAGES ARE RESPECTFULLY DEDICATED,
BY HIS SIMKKi: AND OBLIGED FRI1

THE AUTHOR.

PREFACE.

THE following work has been compiled at the instance
of the Board of Trinity College, and published at their
expense, for the use of the Students in the School of En-
gineering connected with the University of Dublin, and
also of such students in Arts as may take up the subject
of Experimental Physics for their degree.

The object of these pages, therefore, is not only to
convey a knowledge of the leading facts and general laws
<>f the Science of which they treat, but also to assist in
the task of mental training and discipline, which forms
an important feature of University education. With this
object in view, the author has described, as fully as the
limits of the work permitted, the details of the principal
experimental methods which have been employed in the

in ination of the phenomena of heat, has pointed out

disturbing causes complicating their results, and,

where their object has been to obtain numerical values,

lie ! Lained the mode of investigating the formula;

which connect such values with the data of experi-

nt.
And here it may be remarked, that the introduction

of the experimental sciences into the rniver.-ity C1oui>«

Vlll PREFACE.

has supplied an important omission which formerly ex-
1 in that system, by furnishing examples of the ap-
plication of the rules and principles of the inductive
philosophy. For, to adopt the quaint but expressive
image of Bacon, the human mind is so devoted to the
worship of various intellectual idols, that it requires not
merely to have the true object of its allegiance brought
before its view, but also to have its erroneous tendencies
counteracted, and its evil habits reformed, by a system
of discipline adapted to promote the formation of cor-
recter habits.

It is true that, until a comparatively recent period,
few of the Experimental Sciences were sufficiently ad-
vanced to admit of their introduction into the University
Course, with the object above referred to. The funda-
mental laws of most of them were very imperfectly un-
derstood, many were disturbed and obscured by conflict-
ing theories, and all were in a state of rapid progression
and change. Owing to the exertions of the distinguished
physicists, however, who have rendered the past years
of the present century for ever memorable in the annals
of experimental philosophy, the leading principles of the
more important of the Physical Sciences are now esta-
blished by such evidence as entitles them to rank, in
point of certainty, with the deductions of the Abstract
Sciences, and to justify their being referred to as the au-
thentic results of a correct system of physical investiga-
tion.

Although the present work, however, has been spe-
cially designed for a particular class of students, the
author trusts that it will not be devoid of interest to the
general reader. No pains have been spared to collect
the latest and most accurate information on the subjects

PREFACE. IX

of which it treats, and much of the matter which it con-
tains is now for the first time presented to the public in
a connected form.

Several of the Tables in the following pages will be
regarded with interest by experimental physicists in
different departments, especially those which exhibit the

tic force of aqueous vapour derived from M. L
nault's experiments, and expressed in English measures.
There can be little doubt that the experiments on which
those tables are based are the most accurate which have
hitherto been made in reference to this subject, and it
is probable that a considerable time will elapse before a
similar series will be undertaken by an experimenter
combining so much acquired skill and natural aptitude
for physical investigation, with the facilities and advan-
at M. Regnault had at his command.

The author cannot omit this opportunity of acknow-
ledging his obligations to Dr. Apjohn, Professor of Che-
and Mineralogy to the School of Engineering,
for much useful advice and many valuable suggestions
kindly furnished by him during the progress of the fol-
lowing -ln-ets through the Press. The author owes a
similar acknowledgment to S. Downing, Esq., Assistant
Professor of Engineering in the same School, in reference
to the concluding paragraphs of Book I. chap. i. sect.

October, 1849.

CONTENTS.

N*. B. —All students presenting themselves for examination in Experimental Physics are required
to be acquainted with the subjects contained in the paragraphs marked with an asterisk ; candidates
for Honors alone are expected to be prepared in the remainder.

INTRODUCTION.

SECT. I DEFINITIONS. DIVISION OF THE SUBJECT.

PAGE.

i.* Definition of Heat, i

2.' Definition of Quantity of Heat, ib.

3.' Definition of Temperature, 2

4-6.* Division of the Subject. Two Effects of Heat noticed in the follow-
ing Work : i, Change of Temperature ; 2, Change of Volume and

State, 3

7.' Extent and Importance of Subject, 6

SECT. H. CONSTRUCTION AND USE OF THE THERMOMETER.

8.* Measure of Temperature necessarily arbitrary. Measure adopted, . 7

9.* Mode of determining the Temperature of a Body, 8

10.' Principles on which the Comparability of Thermometers is founded, . ib.

it.* Mat. rial of Thermometers, 10

12." Construction of Mercurial Thermometers, n

M. thud (,f dividing the Tube into Portions of equal Volume, .... ib.

M.-tliiMl of tilling ami scaling the Tube, 13

Method c.f nl,tainin^ the lixrd Points on the Scale ib.

Method-, oHIrailujitioM. Fahrenheit's, Celsius', and Reaumur's, . . 15
1 <•! '(!• •(< -nnining corresponding Temperatures on the different

Seal- ib.

18. C ct Assimilation in the Determination of Tempe-

16

; !ninati-.n «>f Length .it >tnn necessary for a given Range, ... 20

20.' Displace™. il>.

II

CONTENTS.

BOOK I.

ON THE RELATION BETWEEN THE TEMPERATURE OF BODIES AND THE STATE OF
AGGREGATION OF THEIR INTEGRAL MOLECULES.

CHAPTER I.

ON THE RELATION BETWEEN THE TEMPERATURE OF BODIES AND THEIR VOLUME.

SECT. I DILATATION OF SOLIDS.

PAGE.

22.* Definitions, 23

23.* Mr. Ramsden's Method of determining directly the linear Dilatation

of solid Bodies, 24

24.* MM. Lavoisier and Laplace's Method, 28

25. M. Pouillet's Method, 30

26. Mr. Daniell's Method, 31

27. Mr. Adie's Method, 33

28.* Remarks on the preceding Methods, 36

29.* M. Borda's comparative Method, .|k. ib.

30.* Method of determining the cubical Dilatation of Glass, 37

31.* Method of determining the cubical Dilatation of Metals, &c., .... 39

32.* Laws of Dilatation of Solids. LAW I., 40

33.* LAW II., 42

34- LAW IH-» 43

35-* LAW IV., 45

36.* Expression for the Volume, &c., of a Solid at any Temperature, in

Terms of its Temperature, Coefficient of Expansion, and Volume

at a given Temperature, 46

37.* Remarks on the Values of the Coefficient of Dilatation of various So-
lids, 48

SECT. H DILATATION OF LIQUIDS.

38.* Definitions. Relation between Coefficients of apparent and real Ex-
pansion, 49

39.* MM. Dulong and Petit's Method of determining the Dilatation of Li-
quids, 50

40.* Method of Densities, 53

41. Method of graduated Tubes, , 55

42.* Laws of Dilatation of Liquids. LAW I., 59

43.* LAW II., — 64

44. Formulae representing absolute Dilatation of Liquids, 66

45. Graphic Representation of Curve of Dilatation of Liquids, 67

46. Relation between the Temperatures corresponding to apparent and

absolute Maximum Density, ... 68

47. Absolute Dilatation of Mercury, &c 69

47, bis. Comparative Contraction of various Liquids, starting from their

respective Boiling Points, 74

COXTK Kill

SECT. IU.— DILATATION OF GASES.

r \«.i .

48.* Notice of early Experiments, 76

49.* M. Gay-Lussac's Experiments, 77

50.* Dr. Dalton's Experiments, 79

51.* Recent Experiments by Rudberg, &c., ib.

52. Apparatus employed by M. Regnault for determining directly the Dila-

tation of Air under a constant Pressure, 80

53. Apparatus employed by M. Regnault for determining the Dilatation

of Air from its Change of elastic Force, 84

54. Modification of this Form of Apparatus, adapting it to the direct Mea-

surement of the Dilatation of Air under a constant Pressure, ... 86

55. Application of preceding Methods to other permanent Gases, ... 88
56.* Laws of Dilatation of Gases ; i, under the atmospheric Pressure, . . 89

uler Pressures greater or less than the atmospheric, .... 91

SECT. IV ON THE COMPARABILITY OF THERMOMETERS AND THE MEASURE OF

TEMPERATURE.

58.* Mercurial Thermometers, 92

59.* Air Thermometers, 94

60.* Comparative Indication of Mercurial and Air Thermometers, .... ib.
6 1 .* Changes of Temperature, as measured by Air Thermometer, formerly
supposed proportional to the Quantities of Heat producing those

Changes 95

62.* Determination, on this Hypothesis, of the absolute Zero, 96

63.' Concluding Remarks on the Measure of Temperatures, ib.

SECT. VI. — APPLICATION OF THE LAWS OF DILATATION.

64. Measures of Length and Weight, 98

65. Units of Length and Weight anciently adopted, 99

66. Attempts to fix Standards of Length and Weight in England. Par-

Ham* ntary Committee of 1758 ib.

I ). -termination of Standards in France 101

68. Determination of Standards in England 102

.absolute Weight and Wright in Air, how afl<

by I .iv 104

70.* Relati. >n li.-twe.-n tabular Density and Temperature 105

• •I* Bar itric Heights for Temperature 108

72.* Correction of M. a-un •- «>f I,< -n^th i'<>r T« •mjirrature ib.

hanges of T'-mp' ratuiv on «t Time no

:i, 112

Compensation Pendulum ib.

ndulum M ;

isgon's Gridiron P« -minium, . . 114

Compensation IVndulum \\ith <
1

XIV CONTENTS.

TAOR.

80.' Pyrometers. Wedgwood's Pyrometer, 116

8 1.* M. Guy ton do Morveau's Pyrometer, 117

82. Mr. Daniell's Pyrometer, 1 1 1

83. Air Pyronu'ttT 118

84. Breguet's Metallic Thermometer, ib.

85. Force of Expansion and Contraction of Metals on Change of Tempe-

rature, 119

86.* Allowance to be made for Expansion and Contraction of Rails and

Pipes, 122

87.* Effects of Expansion and Contraction on arched Bridges, 123

88.* Allowance to be made for Expansion and Contraction in the Case of

Tubular and Lattice Bridges, 124

89.* Effects of unequal Expansion and Contraction in Machines, &c., . . ib.

90.* Effects of Change of Temperature on Buildings, 1 25

CHAPTER II.

ON THE RELATION BETWEEN THE TEMPERATURE AND THE STATE OF BODIES, AND ON
TUB LAWS OF VAPOURS.

SECT. I LIQUEFACTION AND SOLIDIFICATION.

91.* Solidity dependent on Temperature, 126

92.* Phenomena accompanying Liquefaction, 128

93.* Phenomena accompanying Solidification, 129

94. • Abrupt Change of Volume accompanying these Changes of State, . 130

SECT. II VAPORIZATION AND LIQUEFACTION.

95.* Definition and Measure of the Tension or elastic Force of Gases, . . 131

96.* Division of Gases into permanent Gases and Vapours, 133

97.* Relation between the elastic Force and Density of Gases. Boyle's and

Mariotte's Law. M. Regnault's Investigations, 135

98.* Vaporization by Ebullition, 140

99.* Influence of Pressure on Temperature of Ebullition, ib.

100. Phenomena presented by Liquids raised to very high Temperatures

in a limited Space, 143

i oi.* Influence of foreign Bodies on Temperature of Ebullition. Theory

of M. Magnus, 144

102.* Theory of M. Donny, 146

103.* Vaporization by Evaporation, 149

104.* Heat absorbed in the Formation of Vapour, ib.

105.* Leidenfrost's Phenomenon, 150

1 06. I. Assumption of spheroidal Form by small Masses of Liquids pro-

jected on hot Surfaces, 151

107. II. Non-Establishment of thermic Equilibrium in this Case, .... 153

SECT, in LAWS OF VAPOURS.

108.* General Properties of Vapours : A. In vacua, 158

109.* B. In a Space filled with a permanent Gas, 160

CONTENTS. XV

PAGE.

no.* Relation between the elastic Force and Temperature of Vapours at

their maximum Density. Absolute Density of Vapour, 161

in. Expression for the Density of a Vapour referred, i, to dry Air at a
determined Temperature and Pressure; 2, to its own Liquid at a
given Temperature, 162

1 1 2. • Connexion between the elastic Force and Density of Vapours, ... 164

SECT. IV. — EXPERIMENTAL RESEARCHES ON THE ELASTIC FORCE OF VAPOURS.

113. M. Ziegler's Experiments, ib.

114. M. Betancourt's ditto, 165

115. M. Volta's ditto, 166

116. Dr. Robinson's ditto, 167

117.* Mr. Dalton's ditto, ib.

n8.« M. Gay-Lussac's ditto, 169

119. Mr. Ure's ditto, 170

120. M. Despretz' ditto, ib.

i2i.» French Commissioners' Experiments, 171

122. American Commissioners' ditto, 174

123. M. Magnus' Experiments, 175

124." M. Regnault's ditto, 176

125. Experiments of Sr. Avogadro and M. Regnault on the Tension of Va-
pour of Mercury, 183

SECT. V EXPERIMENTAL RESEARCHES ON THE DENSITY OF VAPOURS.

126.' Theoretic Determination of the Density of Vapours from M. Gay-
Lussac's Law of Volumes, 185

iy-Lussaf's Method of determining experimentally the Density

of Vapours, 187

128.* M. I>.-pr,-t/' M.-thod 190

129.* M. Dumas' Method

130. Formula- of Calculation applicable to M. 1 >umas' Method 10.4

131. M. Regnau mining t!:<

pour; I. in vacua, (a) at the Temperature oflm'.ling Water, and
limit r feel. It • I' 198

132. (/?). Within a limited Range of T« mp«-ratuiv on either Side of that

of the surrounding M|dium, and at 1' '-adually «limini>hing

mum, . . 204

133. II. In .I//- in a St. it«- of Saturation . 206

134. Researches mi the Application of tli>

minati-'n of tl; ' : i i

SECT. \ : \i-nn « OMI i i \ri i;i

• |u-..|.al.lr \ .iliii I ••!
from tlh- .1. tu il ({. 210

xvi CONTENTS.

PAGE.

136. Rules for determining the most probable Value of a sinyle observed

Quantity deduced from the Method of least Squares, 222

137.* Method of correcting the observed Values of a Series of Quantities

dependent on a single Variable, 225

138.* Methods of Interpolation by graphic Construction and Formula}, . . 227

139. Methods of calculating the Constants in Formulae of Interpolation, . 228

140. M. Regnault's Method of graphic Construction, 229

141-7. Classification of Formulae of Interpolation for the elastic Force of

aqueous Vapour, 231

148. M. Regnault's Formula-, 242

149. Formulae for the elastic Force of the Vapours of various Liquids, . . 244
150-1. Explanation of Tables I.-X 245

WE give the following account of the French system of weights and mea-
sures, in consequence of their frequent occurrence in the present work.

Modern French System.

In this system the Metre is the unit of length. Its successive subdivisions,
according to the decimal scale, are designated by the Latin prefixes, Deci-,
Centi-, Milli-, and its multiples by the Greek prefixes, Deca-, Hecto-, Kilo-,
Myria- ; thus a Decimetre is the tenth, a Centimetre the hundredth part of a
metre, and a Decametre and Hectometre are equal to ten and one hundred metres,
respectively. This mode of expressing the divisions and multiples of the re-
spective units is carried out through the whole of the modern French system.

The Are is the unit of superficial measure ; it is a square of a decametre
on the side.

The Stere is the unit of solid measure ; it is a cube of a metre on the side.

The Litre is the unit of measures of capacity ; it is a cube of a decimetre on
the side.

The Gramme is the unit of weight. It represents the weight of a cubic cen-
timetre of distilled water at its greatest density. These quantities may be re-
duced to their equivalent values in the English system by the following relations :

1 1 system
English i

i Metre = 39.37079 Ejlglish inches,
i Litre = 1.760759 ,, pint,
i Gramme = 15 .433 ,, grains.

Old French System.

In this system the Toise was the unit of length ; it was divided into six /'rtV,
each foot into twelve inches, and each inch into twelve lines.

Tin- toix.- equalled 76.73336 Knglish inches, and consequently the old French
inch w.is e<|iial to 1.06574 Knglish inch.

TREATISE ON HEAT.

INTRODUCTION.

SECT. I. DEFINITIONS.— DIVISION OF THE SUBJECT.

i. Definition of Heat.. — The word Heat is used in the English
language to denote botli a well-known corporeal sensation and also
the external cause to which we refer that sensation and var
physical phenomena. Some writers have proposed to employ the
; Caloric in the latter sense, and to restrict the word Heat to
former ; but as such practice does not appear to have met with
general approbation, and as no ambiguity seems likely to ,.
from using the word Heat in both senses, we will throughout the
following Treatise employ this word to express the cause of the
corj- Cation, as well as that sensation itself.

The physical phenomena referable to the agency of this <
triking and numerous. Before proceeding to de-scribe thorn
in detail, it appears adraable t<> lay before the reader a sketch of
<xl which we intend to adopt in treating of them, and
also to explain soim- t- mis of more frequent occurrence.

'•/'/ of II' any j-liy-

M is indicated by 6 of the ellects which we

. ami it- . 1 by tin- inten>it\

fc8. In the 0886 oi'heat, the sensation produced by it i
and StrUl :id the |] i that M

.

produced by th
I)

2 DEFINITIONS. [iNTROD.

source in which it resides, to our organs, and that the intensity of
tlii' smsation depends on the force with which the transfer is
made. If, moreover, we observe two bodies, placed in the imme-
diate vicinity of each other, in which the force of heat, thus mea-
sured, is found to be different, we uniformly find that the hotter
body transfers or communicates to the colder a portion of its force,
and at the same time decreases in volume. We are hence led to
speak of heat as of something which may exist in bodies in diffe-
rent quantities, which may be subtracted from, or added to them;
and the same body is said to possess a greater or less amount of
heat according as it possesses the power of producing the sensation
of heat with greater or less intensity.

3. Definition 'of Temperature. — What the actual amount of
heat, thus understood, may be, which a body possesses under or-
dinary circumstances, or what amount it is capable of containing,
we have no means of determining with certainty. Experiments
prove that this amount is very considerable, compared with the
quantities added and subtracted by the ordinary operations of
heating and cooling. We are able, however, to measure and com-
pare the quantities by which, under various circumstances, this
unknown total amount is increased or diminished ; and we learn
from experiment that the addition of equal quantities of heat to
different bodies affects in very different degrees the energy with
which they effect the transfer of a portion of the force residing in
them to other bodies. This is obvious in the case of unequal
masses of the same material. The same quantity of heat which
sensibly increases this energy in a small mass scarcely at all affects
it in a larger, and it is also true in equal masses of different mate-
rials. The quantity of heat, therefore, in different masses, which
produce the sensation of heat in the s'ame degree of intensity,
may be very different. We are to distinguish then between the
quantity of heat in different masses, and the energy with which
this quantity seeks to effect a transfer of a portion of itself to our
organs or other neighbouring bodies. To this energy we give
the name of Temperature ; and two bodies arc said to possess the
same temperature when the quantity of heat in one of them acts
with the same energy or power of transfer and communication as
the quantity of heat in the other, although those quantities may be

IMHOD.] DIVISION OF SUBJECT. 3

different in amount. Thus if two bodies A :uul l\ are placed
in the vicinity of each other, and it' A transfers in a given space
uf time to /> the same quantity of heat as l» transfers to A, which
is known by the heat in .1 and />' respectively retaining its origi-
nal intensity, the 1 is said to be equal to that of
/*'. although the amount of heat in each may be very different.
And if .1 transfers more heat to 13 than l\ to A , which is known
by the intensity of the heat in 23 increasing, then the temperature
«f .1 is said to be greater than that of 7;', although the amount of
in II may be equal to or greater than that in A. To speak
popularly, it appears that a given quantity of heat acts outwardly
with di lie rent degrees of intensity when placed in different bodies ;
and as we must suppose that the total effect of a given quantity of
heat is always the same, we are led to conclude that in dillcivnt
bodies different proportions of this force are absorbed in over-
ing internal resistances, and therefore that the balance free to
'i/tir,//;//// varies in different cases. The temperature of a
l»odv, therefore, may be defined to be the energy with u-hich t/te
/'/ act* i/t tlt': u'ii>/ of ' traiixfci'i'inij or coimnu)w'uting a

Instruments iir-ed for the determination of temperature are
called th. ;iid those for measuring the quantities of

added to or subtracted from bodies, calorimcfsrs. The con-
struction »»f the latter will be described in the course of the work,
• n requires; but as n<> pi-ogre.-* can he made in the
tin- phenomena of heat without a knowledge of the means
employed for determining the temperature of bodies, we will
•te the next section to a description of the principles ..n
which them, are constructed, and the method of their

application to the meuMire of temperature.-, although in doii

hall lie unavoidably t ipelled to anticipate re-nits developed

:ieiit portions of the work.
4. / ' //. dt >«>//,;,/ in the

//./ ( '/in it'. I

N' '• Of I 6 I d»le to the agency of

:>urpo>e to direct the altenli. I the ,-tildent ill the lollov

t to two. M.Ulielv. the rhailLre> plodllod I ' '. 'II ill llie

t<')n; i in the .-la1. '.ion of the'n

4 DIVISION OF SUBJECT. [iNTROD.

integrant molecules. In most cases these two effects are co-
ordinate. When in a solid body, for instance, the quantity of
heat which it contains is increased, its temperature rises, and the
mutual distance of its molecules being at the same time increased,
olume is enlarged ; and this gradual increase of volume and
of temperature accompany each other, until a certain limit is at-
tained, constant in the same, but varying in different bodies,
when a change in its molecular structure commences, known by
the name of a change of state. While this change from the solid
to the liquid state is in progress, the temperature of the body re-
mains unaltered, and the total action of the increased quantity of
heat communicated to the body is exhibited in the alteration pro-
duced in its molecular constitution. The change to the liquid
state having been completed, the action of heat again exhibits
itself in the double effect of increased temperature and increased
volume, until a second limit is attained, at which the transition
from the liquid to the vaporous or gaseous state takes place.
The phenomena accompanying this change are similar to those
attending the former. Between and beyond those limits the
change of volume which, as we have remarked, always accom-
panies change of temperature, is gradual and slow, but at those
two points a brusque and abrupt change occurs. At the former
limit, owing to certain disturbing forces, to which we will subse-
quently refer, this change is sometimes in the direction contrary
to the general analogy, which, as we have said, connects increase
of temperature with increase of volume; but in the transition
from the liquid to the vaporous state, the change of volume is
always in accordance with the general law, and is, moreover,
very considerable in amount. So that if we draw a base line
xy (Fig. i), the distance of successive points of which from any
fixed point a, shall represent the temperatures of a body count-
ed from some given temperature as origin, and erect ordinates
aAy bB, cC, &c., representing the volumes occupied by the body
at the origin, and at the temperatures corresponding to «6, ac, &c.,
the progress of the increase of volume, in relation to the increase
<M temperature, will be represented in most cases by a figure
similar to ABCDEFGH. The temperatures ad and of are those
at which change of state occurs ; and the abrupt rise in the ordi-

INTROD.] DIVISION OF SUBJECT. 5

B from D to E, and train F to 6r, murks the sudden inci-
• liime unaccompanied by change of temperature, which, as
wo have remarked, characterize* those transitions.

The object of tin- First Book of the following Treatiae will be

t-> in- the relations which exist, in various bodies, between

their temperature and volume, between and beyond the poiir
which change of state occurs (Chap, i.); and secondly, to ascertain
the temperatures at which these changes take place in different
bodies, the phenomena which accompany them, and the relations
I Between the temperatures of vapours and their elastic force
and density (Chap, n.) So that the subject of this Book, in faet.
will be, first, the relation existing between those two effects o£ heat
abov. d to, namely, change of temperature and change in

the state of:.. >n of the molecules of bodies, when they

occur together; and secondly, the phenomena which attend, un-
der peculiar circumstances, the exhibition of one of those effects

5. Having in the First Book considered these effects in rela-
to one another, we will proceed, in the Second, to consider
them in relation to their common cause. Experiments prove that
quantity of heat necessary to produce a given change of tem-
aire in a given mass, varies according to the material of which
composed. The ratio of this quantity to the quantity re-
quired to produce the same change of temperature in an equal
B of some material selected as the standard, is called the
'•'^ofthcsu \amination. Thesui

•upy tin- i'nst chapter of this Hook

observed (4) that while a body is undergoing a change

of State its temperature remains unaltered; the quantity of heat,

U) a body during the pn>gre.-s of this change, not

••inwardly, is .-aid to 1 >dv ;

;itution, it is

also called r heat. The .-econd chapter of |>. >» >k II.

will In- occupied with the Mibject of latent or constituent heat.

••ml Hook, thcrefoie, will be, th
ihe qiianlity of heat communicated to a Ljiveu

!il>t, \\hen that etl'eel 1- tWofiild.

iuperatuj. '-alar

6 DIVISION OF SUBJECT. [iNTROD.

arrangement ; and secondly, when that effect is exhibited by the
latter change alone.

6. Having then treated of these two effects of heat, in relation
to one another (Book 1.), and in relation to their common cause
(Book II.), we purpose in the Third Book to inquire into the laws
which govern the transmission of this force, whether through pure
space or intervening bodies, by the way of radiation (Chap. I.),
or along the particles of bodies by conduction (Chap, n.) ; and in
the Fourth Book to give a brief sketch of the theory of the
transmission of heat. A short account of the principal sources of
heat and cold, and of the application of the laws of heat to
Hygrometry, will occupy the Fifth and last Book.

7. Extent and Importance of the Subject. — It will be seen from
this sketch that we do not propose to refer to any of the chemical,
optical, or electrical properties of Heat. We intend to confine
our attention solely to the action of this force on the integrant
molecules of bodies, leaving the consideration of the manner in
which it affects their chemical affinities, and modifies the action
of light and electricity, to treatises on those subjects. Its con-
nexion also with the sciences of meteorology and physical geo-
graphy will be but slightly touched upon in Book V. Even with
these limitations, however, the subject is one of considerable ex-
tent, and of great interest and importance. As we proceed in our
investigations, we will be led to regard heat as the great anta-
gonist of the force of cohesion, — capable, if its amount were
increased, of converting the solid earth into a limitless mass of
vapour, — and by its presence alone preventing the atmosphere
which surrounds it from being condensed into a crust upon
its surface, and the globe itself from being compressed into an
atom. It is the strong repulsive force which it communicates
to the particles of matter, which renders heat so effective as a
motive power, and has enabled modern ingenuity to obtain such
a mastery over the elements of matter, as virtually lengthens life,
and gives men more than the fabled power of giants. To tin1
Kii'jineer, its study, then, is of the utmost importance. Heat
is, so to speak, the life that animates the machines which are
his agents in the accomplishment of the stupendous feats he is
now daily called upon to perform. To the Physicist the subject

INTROD.] CONSTRUCTION AND USE OF THE THERMOMETER. 7

is one of no ordinary interest, as it presents him with some most
beautiful experimental inver.tigation.s of the laws of Nature, and
with results of the utmost elegance and simplicity; while the
y which has been advanced to account for the phenomena
accompanying the transmission of heat opens a most interesting
and profitable field for the investigations of the Mathematician,
and, like the theories of the other physical sciences, has led to
some of the most important discoveries in pure mathematics.

SECT. II. — CONSTRUCTION AND USE OF THE THERMOMETER.

8. Measure of Temperature 'arbitrary; Measure <
The temperature of a body is, as we have stated, the force with
which the heat present in it seeks to transfer a portion of itself to
hbouring bodies. In different masses of matter this force is a
function of their weight, of their specific heat, and of the total
quantity of heat present in them; in the same mass, therefore, it
simply varies with the quantity of heat which it contains.

;ave no direct means of measuring the energy or intensity
of this force in a given body; failing this, our simplest liypotl
would be to suppose it t«> lie /m-y^y/^/^/ to the quantity of heat
which it contains, and therefore the least arbitrary mcasui-

:igcs of temperature in any body would be the corresponding
changes in the quantity of heat present in it. Such a mea>ure, how-
M he highly inconvenienl in n. >nd impracticable

in many, and then-fore we arc compelled to look out for one more
convenient in its application, although, perhaps, more arbitrary
in its nature: and this we find in the chair '.nine, which,

as we have remarked, is always co-ordinate with dun. mpe-

rienoe ]•: .it the same body all

volume at tlie >ame temperature, provided that

during tin- alterations of temperature to which it d it

• loss of substance or peculiar < IK ular

• llo\v> that the volume of a bndv is the exponent

trary
• mer.

r fulfill: and

'

8 CONSTRUCTION AND USE OF THE THERMOMETER. [iNTROD.

ture which it is required to measure, are either sufficiently consi-
derable to be easily observed, or are capable of being rendered so
by some mechanical contrivance, will serve as a thermometer,
which may be described as an instrument employed for the deter-
mination of temperature and the measure of its changes.

9. Mode of determining the Temperature of a Body. — To un-
derstand the use of this instrument it is to be remarked, that if
two bodies of unequal temperature be placed in contact, the body
whose temperature is higher communicates more heat to the other
than it receives from it in a given time, and that thus, after a short
time, the temperatures of both become the same. If, therefore, we
place a thermometer in contact with the body whose temperature
we desire to ascertain, after a certain space of time has elapsed,
it acquires the same temperature with the latter, and indicates that
temperature by the volume which it occupies.

It is to be remarked, however, that the temperature thus de-
termined is not the original temperature of the body under
examination, but its temperature after, by mutual transfer of dif-
ferent quantities of heat, it and the thermometer have acquired a
common temperature; it is, in fact, this common temperature
which we ascertain, which will be greater or less than the origi-
nal, according as the body examined has received or parted with
more heat than the thermometer during the process of assimilation,
that is, according as it had originally a lower or higher tempera-
ture than the thermometer. This resulting temperature, however,
will differ the less from the original, the smaller the mass of the
thermometer is, as compared with the mass of the body examined ;
and we shall accordingly assume, for the present, that the mass of
the thermometer is so small that the quantity of heat necessary to
be transferred to or from the body under examination, to equalize
the temperatures, does not sensibly affect the temperature of the
latter. We shall see subsequently (Book II. Chap, i.) how we
can altogether remove the inaccuracy arising from this source.

10. Principles on which the Comparability of Thermometers is
founded. — For the purposes of individual research, therefore, any
body fulfilling the conditions above referred to will answer as a
thermometer, and any scale applied to it, indicating its volume
at a given time, will serve to determine the corresponding tern-

IXTROD.] CONSTRUCTION A MI 1's.E OF THE THERMOMETER. 9

uire, and to measure its changes. But in order that different
: vci's should be able to compare their results and experiments,
it is neces.-arv that the indieations of different thermoni-

Id be comparable. IIo\v this is effected we proceed now to
lain.

3 prove that it' different masses of tlie same ma-
eoinimni temperature, the >ame dl

tun.' produce- in them changes of volume proportional to their

Hal volumes. Thus if, at a common temperature, which we

-hall denote by the symbol r, we have two masses of the same

material, whose volumes arc v and r, and if. on raisiiiij them both

mperature r, the increments of volume are $r and

5* S1 '

ve have always c/-.- c'- :: o: r, or — = — r5 and conversely, it'
this analogy holds, and if the temperatures corresponding i
and '• are the sime, then tlie temperature eorrespondin«r to the
volume r - cr is tin- same as the temperature corresponding to
volume v+$v. In order, therefore, that two instruments
should be comparable, it is sufficient to construct them ot
material, to note on the scales attached to them their
vobi! tnc common temperature -. and to divide the s<

e.pud part-, each ofwhich shall correspond to an increment
of volume bearing some L-i\cn proportion to the original vobr

Tor instance, that we take two mas.-rs of the ,-anie material,

lumes at some common temi ire '• ami >• , and

. whoee di ml to iiu-re-

p;i]t of those volumes respectively, so that each di-
11 on one ivalent t«. -, and on the other i

, by one of those masses occupying

!«-es upon its scale, will be th-- I that in-

10 Other occu; .-• number of decrees upon

te <»f volume beini: — and — are ob\i-

' r

either be effected by dll MIH>-

I.ei ihe FoltUnet '• and

common temperature r. be mai
c

10 CONSTRUCTION AND USE OF THE THERMOMETER. [iNTROD.

on scales applied to them ; let the volumes V and V, occupied
by the same masses at a higher common temperature, be also
noted on the same scales ; from what we have said it follows that
the intervals on the scales between those two points correspond
to increments V- v and V - v, which are in the ratio v:v; and
those intervals, or any convenient aliquot parts of them, may be
assumed as the units of division. Suppose we divide the space
occupied on the respective scales by the increments V-v and
T'-rinto s parts, and assume one of these as the unit, then

TT rr> / V-V V'-V

since y-v: V -r::v:0, we have : ::v:v, and also

s s

V-v V'-v

n :n ::v:v, and consequently the temperature indi-

s s

cated by one of the masses occupying n degrees on its scale,
thus divided, is the same as that indicated by the same number
of degrees on the other.

The conditions requisite to be fulfilled, therefore, in order to
render two thermometers comparable, are, first, to construct them
of the same material ; secondly, to note on the scales attached
to them the respective volumes corresponding to two constant
temperatures; and thirdly, to divide the intervening portions
of the scale into the same number of equal parts. Sir Isaac
Newton first pointed out the advantage to be obtained by
this method of graduating thermometer scales, and at the same
time proposed as the fixed points in the graduation the tem-
peratures of melting ice and boiling water. His suggestion has
since been universally followed, with some diversity, as will be
mentioned hereafter, in the number of degrees into which the
scale is divided between these two points.

u. Material of Thermometers. — In our choice of the material
of which to construct a thermometer, we must be determined,
among other considerations, by the temperatures required to be mea-
sured by it. Thus if it be required to measure very high tempera-
tures, a refractory metal, as platina, is best suited for the purpose.
Again, if our object be to measure with extreme accuracy small
changes, air or some fixed gas, corrected in its dilatations for altera-
tions of barometric pressure, is most suitable ; while for ordinary
purposes some of the liquids which expand more than solids, and do
not require the corrections necessary in the case of gases, are found

INTROD.] CONSTRUCTION AND USE OF THE THERMOMETER. I I

to answer best. Of all the thermometers of this class, that con-
structed with mercury contained in a glass envelope is most gene-
rally used; we will accordingly select it as an example, for the
purpose of describing the mode of construction, graduation, and
use of this important instrument.

12. Construction of M Thermometers. — The mercurial

thermometer is formed of a glass tube with a fine cylindrical
bore, sealed at one end, and terminating at the other in a ball or
reservoir of large capacity, containing the mercury. By this ar-
rangement one of the requisites above referred to is satisfied,
namely, that small changes in volume of the thennometric
suhstance should be rendered sensible; for the volume of the
ball being very considerable compared with that of any length
of the bore, a small increase in the volume of the liquid con-
tained in the former fills a considerable length in the latter.
This eileet is increased in some instruments by using a bore
of elliptical, instead of circular, section; the minor axis being
almost evanescent, the area of the bore is greatly diminished,
while the plane passing through the major axis being per-
pendicular to the line of vision, the mercury is even more
ptible than in a tube of circular section with greater capa-
It is to be remarked, that as the glass envelope expands
with an increase of temperature, as well as the mercury it con-
tains, the expansion of the latter which is observed, or, as it is
^parent expansion of the mercury, is the difference
• •en its actual expansion and the expansion of the glass en-
e, as will be explained more fully in the next chapter.
13. M. tit' "I "/' Jii-'uliiKj th<: Tnln' info L\irt'nmx of equal Volume. —
It has br. i that the mode of gradual. thermon

is to divide the I] '.nines it occupies, at tWO

.peraturos, into a irm-n number of portions of c-junl
would h.- Hl'ecied, iii the case of mercurial thermo-
niplv di\ idiii!_r the portion of the tube Q the

tfl at which the mercury Mands at the two temper;,:

to, into the given number of ] •'//, ifthe

bore wen- truly cylindrical, and this i- the way in which thermo-
i ordinary lift . i '. .: • inu-t he

1 in the graduation of inurnment- employed for pui;

1 2 CONSTRUCTION AND USE OF TIIE THERMOMETER. [iNTROD.

where extreme accuracy is required. For these the tube should
be divided into portions of equal volume by the following method,
due to M. Gay-Lussac.

A tube having been selected as nearly uniform in bore as
possible, a quantity of mercury is introduced into it, so small that
the space it occupies may be considered, without sensible error,
as perfectly cylindrical. The extremities of this space, as i , 2
(Fig. 2), are marked on the tube with a diamond point; the
index of mercury is now moved forward until its left hand extre-
mity, M, coincides with 2 ; its right hand extremity, M', now
marks a point 3, such that the space 2, 3 is exactly equal in vo-
lume to i , 2 ; and this process is repeated until the whole tube
is divided into portions of equal volume. But as it is extremely
difficult to move the column of mercury so that its left end in one
position shall coincide exactly with the point occupied by its
right end in a previous one, the following method is to be
preferred. Draw a line AB (Fig. 3) on a plane surface, and
having moved the column from the position MM' to M" M'", so that
M" is as near to M' as possible, mark the corresponding length ju//
on the line AB, next bring the point 2 on the tube to coincide
with jit, and p will then mark the point 3. The further subdi-
vision of the portions i , 2 ; 2, 3 ; &c., may be effected by simply
dividing them into portions of equal length, as they are supposed
to be perfectly cylindrical.

These divisions of equal volume will probably not agree in
number with the degrees into which, as we have said, the
space between the points at which the mercury stands at the
two fixed temperatures is to be divided ; it is easy, however, to
ascertain the number of degrees to which any given number of
divisions corresponds. Thus let JV be the number of degrees
between the fixed points, N' the number of divisions on the tube
between the same points, then the number of divisions in a de-

N'
gree is -^, and therefore any number ri of divisions corresponds

N

to ri -jrp degrees, and a number n of degrees is equivalent to

N' ^
n-rr divisions.

INTROD.] CONSTRUCTION AND USE OF THE THERMOMETER. 13

14. M.tlto'l of jilliifj tiiul Midiwt the Tube. — The tube having

thus divided, the ball is to be blown at its extremity, not,

it in .larked, by the breath, lest moisture should be depo-

in the tube, which it would be extremely difficult to remove,

but 1 - of an elastic ball of caoutchouc tied on one end,

and compressed, when the glass at the other end ha- been ren-

1 sufficiently plastic by heat, care being taken to prevent a

• f the bulb, by admitting air into the caoutchouc ;

through an aperture in itself, on removing the pressure. The bulb

being formed, the thermometer is ready to be filled with mercury,

which should be perfectly pure, and freed from all moisture and

air 1 boiling. The mode of introducing the mercury into

the bulb is as follows: — The bulb being carefully warmed over

the llame of a spirit-lamp, the air within is expanded, and a por-

tion expelled; if the end of the tube be now plunged into the

prepared mercury, when the air in the bulb cools it will contract

in volume, and its place will be supplied by mercury, which will

!ly rise through the tube and enter the bulb: this operation is

to be repeated until a sufficient quantity of mercury has been intro-

1. More frequently, however, the mercury is placed in an en-

largement formed at the top of the tube, and the air forced through

heat of the lamp is replaced on cooling by the descent of

•iiercurv. The instrument having been fdled, the mercury is

boiled for a considerable length of time, to remove all air and

• being taken to keep all parts of the instrument at

;< mperature, and not to press the operation too rapidlv.

!io tube is now sealed, to prevent any accidental loss

iorcury, and when sealing, it is desirable to exclude all air,

as its presence in the sealed tube is frequently a soi. n.-i-

e, by breaking up the mercurial column.

usion of v by

. so as to fill the whole of the tube- while the process of -

•. A th. iih which th .tion

has been observed is easily r< .ting the

eury will il')\v t<> 18, it' the

bubble of air has :, it will form an ela-tic cu-hion

1 thcr-

14 CONSTRUCTION AND USE OF THE THERMOMETER. [iNTROD.

mometcr is now prepared for graduation, the first step in which
process is the determination of the fixed points, corresponding to
the two n-i ven temperatures. Of these the lowest is that of im-ltimj
This temperature is absolutely constant, provided only that
the water from which the ice is formed is free from salts; and
the only precaution to be observed in ascertaining the point cor-
responding to it on the thermometer tube is to take care that all
the mercury — that in the tube as well as that in the bulb — is
brought to the required temperature, by keeping the thermo-
meter plunged in the ice up to the point at which the mercury
then stands. The point thus ascertained is to be marked on the
tube.

The second constant temperature is, as we have said, that of
boiling water. More correctly, it is the temperature of the va-
pour of pure water, boiling under a normal atmospheric pressure.
For the amount of the pressure under which water is boiled, the
nature of the vessel, and the presence of salts, all affect the tem-
perature of its boiling point, as will be more fully explained in the
second chapter of Book I. The second fixed point on the scale,
therefore, is not so easily determined as the first ; for as the pressure
under which water is boiled affects the temperature of its boiling
point, and as the water at the bottom of a deep vessel is subjected
to a greater pressure than that at the top, it follows that the tem-
perature of boiling water varies through the several horizontal
strata of the same vessel; and accordingly, if, with the object of
submitting all the mercury to the required temperature, we plunge
the thermometer vertically into boiling water, the mercury in
the different strata will, in fact, be at different temperatures.
It has been observed, however, that the temperature of steam pro-
duced from pure water under a constant barometric pressure is ab-
solutely constant, and hence an easy and simple method is ob-
tained of fixing the corresponding point on our thermometer
scale. A cylindrical tin vessel (Fig. 4), of suitable length, is fur-
nished with a lid containing two apertures ; through one of these
(a\ fitted with a cork, the thermometer tube is passed; the steam,
supplied by a small quantity of water (ef) at the bottom of the
vessel, which, when used, is heated by a spirit lamp placed under-
neath, escapes through the other (/>). The air having been all ex-

INTROD.] CONSTRUCTION AND USE OF THE THERMOMETER. 15

polled and replaced by steam, the thermometer is pushed down into
the vessel according as the mercury rises, the top of the mercury
being always kept on a level with the upper part of the lid, until
it has attained its highest elevation in the tube. By this means, ii'
the process be conducted when the barometer stands at the proper
height, the second iixed point will be correctly determined. If
tion be conducted when the barometer stands at a diffe-
rent height, the correction to be applied to the point deter-
mined by the preceding method will be pointed out in Book I.
. u.

'.i?h physicists have adopted, as the normal pressure for
the graduation of thermometers, that equivalent to a column
of 30 inches of mercury, at the temperature of o° Cent. ; the
-elected, I'm* the same purpose, the pressure corres-
ponding to a column of 760 millimetres, or 29.922 inches, at

iinc temperature.

1 6. JA///o,/x of Gradwit'n.n; Fn/tn'it/n'it'Sj Celsius*, and Reau-
\ pendent of the slight difference in the determination
of the second fixed point, arising from the cause just referred to,
there exists also a diversity in the manner of graduating thermo-
meter scales bittern the two fixed points, and in the selection of
/.ero. Thus, in the scale generally adopted in England, and
1 Fahrenheit's scale, the interval between the two points is di-
l into 1 80 degrees, and the zero is placed at 32° below the
.e<] point. According to this scale, then, ice melts at
32°, and water boils at 212°. Again, Celsius, a Swede, prop
a division of the fixed interval into 100°, and placed the
point. This mode of graduation is called the (
it is universally adopted in France, and recommend^
ML'ly, by its simplicity, for scientific purposes. A third
iiimur's, wh«> divided the interval into Ho°, and iixed
/.ero, as in the Centigrade, at the p«,int ot'melti
i-. .!/. '/< /• / correspou'lii rtf <>u th<

Scales. — It ia easy to determine the p«.int en one oft!
seal corresponds to a given degree upon another. •

<•!' the two la-t mentioned, \\hieli both count

us the same space in the (Vn:
iiieh in Reaumur's is divided into 80°, it

1 6 CONSTRUCTION AND USE OF THE THERMOMETER. [iNTROD.

follows that i°of the lattcr=i°.25 of the former, and, accordingly,
that any number of Reaumur's degrees is changed into the corres-
ponding number of Centigrade, by multiplying them by 1.25, or by
<j _i_ 4, or by adding one-fourth of their number to them. Conversely,
jiuile are converted into Reaumur's by multiplying them
by -8, or by 4 -f- 5, or by taking one-fifth of their number from them.
Again, 180° Fahrenheit equal 100° Centigrade, hence i° Falir.
= |° Cent., and therefore any number of Fahrenheit's degrees is
con verted into Centigrade by multiplying them by 5 -=- 9 ; and con-
versely, Centigrade are converted into Fahrenheit's by multiply-
ing them by 9 -7- 5. But if we wish to ascertain the point on one
scale corresponding to a given point on the other, we must tako
notice of the difference of the zero on those scales. Thus 50°
Fahr. is only 18° Fahr. above the point of melting ice, which is
the zero of the Cent, scale, and accordingly the point of the
latter corresponding to 50° Fahr. is obtained by multiplying 1 8° (or
50°- 32°) by 5 -r- 9, and therefore 50° Fahr. = 10° Cent. ; and simi-
larly, to find the point on Fahrenheit's scale corresponding to a
given degree on the Centigrade, after reducing the number of
Centigrade degrees to Fahrenheit's by multiplying them by 9 -f- 5,
and thus obtaining the number of Fahrenheit's degrees above the
point of melting ice, that is, above 32° Fahr., we must add this
number 32° to the number so obtained, to get the required de-
gree on Fahrenheit's scale. Thus the temperature 15° Cent.
= 15° x 9 -f- 5 = 27° Fahr. above melting ice, or above 32° Fahr.,
and therefore corresponds to 59° Fahr. Hence the following
practical rules :

To convert any Number of Fahrenheit to Centigrade Degrees. —
Multiply them by 5 -r- 9.

To convert Centigrade to Fahrenheit. — Multiply them by 9 -f- 5.

To find the Point on Fahrenheit's Scale corresponding to a given
Degree on the Centigrade. — Multiply the number expressing the
degree Centigrade by 9 -4- 5, and add 32.

To find the Point on the Centigrade Scale corresponding to a
given Degree on Fahrenheit's. — Subtract 32 from the number ex-
pressing the latter, and multiply by 5-^-9.

1 8. Correction for imperfect Assimilation in the Determination
of Temperatures. — In order to ascertain with accuracy the tcm-

IXTROD.] CONSTRUCTION AND USE OF THE THERMOMETER. 17

peraturc of a body by a comparison with the mercurial thcrraome-

t is obviously necessary to bring all the mercury in the latter
to the same temperature with the body under examination. Other-

. if but a part of the mercury is brought to this temperature,
and the remainder continues at the temperature of the surround-

niedium, the observed temperature will be greater or less
than die true, according as the temperature of the surrounding
medium is greater or less than that of the body examined.

re this condition cannot be fulfilled, and extreme accuracy
is required, a correction can be applied by means of which we
may approximate to the true temperature. We will now pro-
ceed to investigate this correction, and first show how the volume
of the bulb of a thermometer, relatively to that of any portion of
its tube, may be determined, as the knowledge of this volume

eessary in the subsequent investigation. There are two me-
thods of determining this volume ; one is by finding the weight
of mercury which fills the bulb, and then the weight which fill?,
in addition, a known portion of the tube at the same temperature.
Suppose the tube divided into portions of equal volume, and take
one of these as the unit of volume ; call V the volume of the
bulb, including the small portion of the end of the tube, where
the bore is conical at its entrance, and let W be the weight of
mercury filling Fand // divisions of the tube, W i ir the wriuht
filling Fund n divisions; then w is the weight of (n -n\ and

the volumes being as their weights, we have V+ n : n - n : : If: *.

II'

and hence I"= — (n'-n) >/.
w ^

second method of determining V depends on the know-

• of the quantity by which nu'ir.urv apparently expands in

: the temperatures of melting iee and boiling water,

oro° and 100° Cent. This quantity, as we .-hall see in the next

••quals I -r- 64. 8th* part of the volume at the lower trmpe-

' T: .v MM. I >u- nearly identical as po»M M.I.

long and Petit (Ann. (L \t\vm(Ann.,i I».Mp*,tM

torae hut a* it depends on p 33;>. f.imid that, even when

the nature of the glass of \\lu.h tin- th.r- th thermometer* which he cn>|>l<>

mometer it constructed, ., :.i:.t !n^ . x laments were composed of the same

quantity, even when all ]>r .• desoripUon of glass (cryttnl, a kind of Hint

ure gt*M of a description as glaM, see Dumas, / ^>imfV, t»inr»

18 CONSTRUCTION AND USE OF THE THERMOMETER. [iNTROD.

rature. Now suppose tlie mercury at o° to fill the volume Fund

;/ divisions, and at 100°, V+ut then (n - n) = - — -, or

64.8

F=64.8 (ri -n)-n.

Now to ascertain the correction to be applied to the observed
temperature in the case of imperfect assimilation, as, for instance,
where the thermometer is but partially immersed in a liquid whose
temperature we desire to know, let AB (Fig. 5) represent a thermo-
meter under such circumstances, immersed to a in a fluid ; suppose
that before immersion the mercury stood at b, marking the tem-
perature t of the surrounding medium, then, if the fluid be of a
higher temperature, the mercury will rise, suppose to c, marking
the temperature t1 ; suppose further, that, if totally immersed, the
mercury would rise to d, marking the true temperature £,., we
require the correction cd. Let F represent the volume of the
part immersed, expressed, as well as the portions ab, be, &c., in
the units already referred to. Now bd is the volume by which
F+ ab expands when the temperature is raised from t to k, and
cd is evidently the quantity by which ac, the portion retained at
the temperature of the surrounding medium, would expand for
the same change of temperature ; and therefore, according to the
law already referred to, namely, that the quantities by which
bodies of the same material expand for the same change of tem-
perature are proportional to their original volumes, we have

be etc
F+ ab:ac::bd:cd'.' cd = ' . A similar process shows that if

the temperature of the fluid be lower than that of the medium,

uC CLC

c'd' = ' . „ in the former case cd is additive, in the latter sub-
v+bc

tractive ; hence the two formulae may be comprehended in the one
expression,

be .ac

by giving the proper sign to be. In this formula cd is the cor-
rection in volume, be the volume by which the mercury rises or

ii p. 614), in as perfect a state of homoge- mits 0.0161154 and 0.0154155, or, in vul-
neity as could possibly be obtained, still 11

the above quantity varied between the li- ' 64.87 ° 62.05*

INTROD.J CONSTRUCTION AND USE OF T11K THERMOMETER. 19

falls, and ac the volume remaining at the temperature .of the

medium. If X represent the volume occupied by a degree, -r-

A

will be the number of degrees corresponding to the volume cd;
and dividing both sides of the preceding expression for cd by A,
and the numerator and denominator of the right hand member
by the same quantity, we get

where %t is the correction in degrees, v the number of degrees
remaining imaasiinilated, Iri the volume expressed in degrees as
units. And as F1 = 6480-71, n being the number of degrees
between a and the zero of the scale, we have

a-

6480- [*+«-<)]'
This correction may be graphically represented in a manner
which may assist the student's memory. Let ac (Fig. 6) re-
nt the length of the column of mercury unassimilated in
temperature, an the length of a similar column equal in volume
in = be, join mCj and draw nd parallel to me; cd is the
correction required. Fig. 6 represents the case in which cd is
additive; Fig. 6, bis, that in which it is subtractive.

It. when graduating a thermometer, we are unable to plunge

the whole of the mercury into the ice or boiling water, the correc-

of the points apparently corresponding to o° and 100° may be

ncd by the same formula. In this case, referring to Fig. 5,

[•aiviit, <l will be the true zero, and c and (/ will l>e

apparent and true boiling points.

It may be remarked that the correction for imperfect assimi-

n of temperature, which is never applied unlc.-s extreme ac-

1, and pei fee t Inatrnmeiitf employed, IB rendered

-sary in ordinary case?, il'the instrument in use hap-
to have been graduated l.v inr..inj.lete immei>i..n. Thus il'

point assumed. lV«.m Mich a melhod of
10O°, and •/ the tine i x '. MipjM.se tliat the nieh to 0 , «-ii

Mj.l.-te immersion, instead "!' u> •/ , tl ec , 01

of fd .

20 CONSTRUCTION AND USE OF THE THERMOMETER. [iNTROD.

19. Determination of Length of Stem necessary for a given
Range. — By a similar method of investigation we can determine
the length of stem to give a thermometer, in order that it may serve
to measure temperatures ranging from t\° below, to t'° above, zero,
and also the height at which the mercury should stand at the time
of filling, to allow of this range. Let ad (Fig. 7) represent the
stem of the thermometer, the divisions commencing from a ; call
the volume below a, V; suppose the mercury at o° to stand at c ;
at the time of filling, when the temperature is t°, let it stand at b •
and at the upper limit t'° at d\ we are required to determine the
lengths ab and ad. As the volume of mercury at o° = V+ ac,

the length of one degree upon the scale equals — — , and there-

6480

t ( V+ ac\ t ( V -\- ac\

fore the length of if = 'v - — — ; hence ac = — — , andthere-

6480 6480

fore ac = — . Similarly as cb contains t°, cb = - , n , and

6480-^1 6480

thus we obtain for ab = ac + cb, the value

ab

6480 - ti

t'( V+ ac)

also ca = — 1 - - ; hence as ad = ac + ca
0480

6480-^1

It is advisable to leave the stem somewhat longer than the
length thus determined, as the dimensions are rendered irre-
gular near its extremity by the process of sealing. It may be
remarked that carefully constructed instruments are generally
finished with a slight enlargement, to allow of the expansion of
the mercury beyond the temperature which they are intended to
measure ; without this precaution, if they were accidentally ex-
posed to a much higher temperature, the expansive force of the
mercury would fracture the envelope.

20. Displacement of Zero. — We will conclude for the present our
remarks on the subject of the mercurial thermometer, by noticing
the discovery of M. Flaguergues,* relative to a change which takes

* Anii;ilc> <!<• Cliiinie ct tit- Physique, tome xxi. p. 333 (1822).

INTROD.] CONSTRUCTION AND USE OF THK TIIKRMOMETER. 21

place in the position of the zero point. It appears from his expe-
riments, since confirmed by M.Legrand,* that all thermometers are
liable to a displacement of their zero after they have been some time
made; that this displacement takes place gradually, proceeding
more rapidly at first, and continuing during a period of from four to

:ionths, until at last the zero stands from o°3 C. to o°5 C. higher
than at first. This displacement appears to be owing to the
circumstance that the glass envelope requires the length of time
above mentioned to contract to the volume which it finally occu-
pies, after the high degree of heat to which it was exposed during
the boiling of the mercury. This explanation is confirmed by
the fact, that if, after the displacement of the zero, the mercury
be again boiled, the zero returns to its original position, and the
phenomenon is clearly connected in some manner with the nature
of the envelope, as it does not occur, at least to the same extent,
in the case of instruments made with crystal glass.f

21. Spirit Thermometer. — The range of the mercurial ther-
mometer extends from about 350° Cent., or 662° Fahr., the
boiling point of mercury, to - 39° Cent., or - 38.2° Fahr., at which
temperature this metal congeals. When approaching this point,
however, its indications become very irregular, owing to the
change of state then beginning to take place in the mercury.
For low temperatures, therefore, we must have recourse to the

: thermometer, by means of which we can estimate the lo

:iable, as the liquid with which it is filled, pure alcohol,
has never been frozen. It does not, however, answer so well to
measure hi^h temperature.-, in consequence of the low position of
its boiling point ; although, if the stem be carefully sealed, and all

xdudrd, this, as well as other liquid thermometers, may be
applied to measure temperatures considerably above those at
which tin- liquid lilliiiLT them boils in the open air. With respect

ie graduation of the spirit thermometer it must be obsen . •«!.

if it be intended to compare its indications with those of the

adu.ited by a compai

nnaka de Chimic et de Physique, thermometer* by thelrwgul.miy in tl

tomelxiiLp. 868 (1886). )iaiisionofU>eir envelope*, and on the com-

r some further remark* on the effect parton of different thermometer*, see Book

• «l on the Indications of mercurial L ehftp. I. ltd

22 IBOJ T1IK TIIKK.MOMKTKH. [iNTROD.

with a carefully constructed instrument of the latter description,
:iparal>ility of instniinents graduated indepen-
dently, it is not only n that their scales should be divided

;i uivc-n number of equal parts between fixed points, but also
that thev should he all formed of the same material, or at least of
matt-rials for which the proportion referred to in (10) holds true
mutually; but this is not the case with mercury and alcohol, or
any other known liquid. This method of graduation cannot be

:idcd, of course, below the inferior limit of the scale of the
mercurial thermometer. Beyond that point the spirit thermo-
meter should be graduated by comparison with an air thermo-

,, t«> be described hereafter, whose indications are almost
identical with the mercurial for a very considerable range of
temperatures.

\Ve will reserve the description of other kinds of thermome-
ters until we shall have investigated the laws of dilatation of the
bodies of which they are composed.

BOOK I.

mi: RKI.UION r.r.rwr.r.x Tin: IDfFBKATUBB OF BODIES ANP nir.

STATE OF AGGREGATION OF TIIKIK IN IT.HKANT Mnl.l ;. li

CHAPTER I.

ON THE RELATION BETWEEN THE TEMPERATURE OF BODIES AND
THEIR VOLUME.

22. Definitions. — It is our object, in the present chapter, to in-
irate the relation between the changes of temperature to which
bodies are exposed, as measured by the mercurial thermometer, and
the corresponding changes which they undergo in volume. W<
purpose to examine this relation in the three classes of bo
solids, liquids, and gases, successively; first describing the prin-
cipal methods of experimenting, with their results ; next stating
the general laws derived from such researches; and finally point-
ing out some of the more important practical applications of those
laws.

It has been remarked, that, in general, when a body receives
an increase of temperature, its volume 18 enlarged, and at tin.- same
time the area of any portion of its surface, and the length of any
of its edges, is increased. The increase of a body in volun
1 its cubical expansion or dilatation, its inerr;ise insm-fae-
superficial, and its increase in length, its If

\v deii'.tr thr value of any of those quantities, namely, the vo-
lume of a hodv, tin- extent of any portion of its surfaee, or the
! i of any of its edges, by the symbol (j. and by // tin- incre-
• whieh this quantity : DO meiva>e of trmj.erat in •-

value will be Q+</, whieh may be put under the form
r), y bring equal to ?u. In t ssion ^ denotes a

senting the fractional j»a: original quantitv

24 THE TEMPERATURE OF BODIES AND THEIR VOLUMES. [BOOK I.

by which it increases for a given change of temperature, and is
called the coefficient of expansion corresponding to the original
quantity and the gir»-n change of temperature. The coefficient of
expansion, therefore, may be defined to be the expansion, corres-
ponding to a given change of temperature, of the unit of volume
taken at a determ ///<'</ temperature. The value of this coeffi-
cient varies in different substances; it also varies in the sumo
substance with the temperature of the original volume, &c.,
to which it is referred, and the extent of the change of temperature
to which it corresponds. The change of temperature is generally
expressed by an inferior index ; thus ST denotes the coefficient of
expansion corresponding to a change of temperature measured by r
degrees. In like manner, if we denote the volume, surface, and
length of a body by V, S, and L, respectively, these symbols are
frequently distinguished by indices expressing the temperature
to which they correspond. Thus V0, Vh Vv represent the volumes
of a body at the temperatures o°, t°, ^°. Following this system of
notation, therefore, we may express the volume, surface, or length
of a body at the temperature t, in terms of its volume, &c., at the
lower temperature t, and of its corresponding coefficient of expan-
sion, as follows:

ST ST', ST" being the coefficients of cubical, superficial, and linear
expansion, corresponding to the original temperature t and to the
change of temperature (t'-t) = r. We now proceed to explain
the method of determining by experiment the values of the co-
efficients of expansion in different bodies, and first in the case of
solid bodies.

SECT. I. — ON THE DILATATION OF SOLIDS.

23. Mr. Ramsderis Method of determining the linear Dilatation
of solid Bodies. — The subject of the linear dilatation of solid bodies
by heat was first investigated, with the degree of accuracy due to
its importance, at the close of the last century. In the year 1782
the eminent French physicists, Lavoisier and Laplace, instituted an

CHAP. I.] LINEAR DILATATION OF SOLIDS. 2$

extensive series of experiments in relation to this subject, the re-
sults of which, however, owing to the melancholy death of Lavoi-
sier at the commencement of the French Revolution, were not
published, we believe, until they appeared, in 1816, in M. Biot's
Traiie de Physique. In the year 1783, Mr. Ramsden, whose
name is well known in connexion with the improvements intro-
duced by him in the construction of various instruments of scien-
tific research, made some experiments on this subject at the re-
quest of General Roy, who was at that time engaged in the
trigonometrical survey of Great Britain. These experiments
were made chiefly with the view of determining the variations of
length to which the rods, employed in measuring the base on
Hounslow Heath, were liable from changes of atmospheric t-
perature ; and accordingly only seven bars, three of brass, one of
steel, one of cast iron, and two of glass, were examined. Mr.
Kiunsden's method of experimenting, however, appears to us to
possess such peculiar advantages, and his apparatus is characte-
rized by such elegance and simplicity, combined with accuracy,
that we purpose to give a brief description of its construction,
referring the student for further details to General Roy's memoir
in the seventy-fifth volume of the Philosophical Transactions.

On a strongly-framed table, of about five feet in length by three
in breadth, were placed three troughs, parallel to one another,
represented in their general plan in Fig. 8. The two exterior
were formed of wood coated internally with pitch, the central
one of copper. The exterior troughs contained each a bar of
cast iron, permanently secured at one end, and moveable through
a collar at the other; the nearer bar, AB, carried at its extremities

vertical frames bearing the eye-pieces, E, E', of two micro-
scopes represented in elevation in Fig. 10, with their axes ho-

ital. and at right angles to the direction of the bar; of these, E
had in its focus t 1 parallel wires, K' two similar wires co-

<>i '!>' 'inor moved by a micrometer sen \\. n, in a j>lai

to the axis. Tin- microscope E' was hence culled

>nicn>met<-r microscope. The larti • n, carried, .-n M-

milar vertical frames, mark-, ;//, m', consisting each of two line
crossed K i in elevation in Fig. 9. Tim central

gh was placed upon rollcre, and was capable ol ovcd

E

26 LINEAR DILATATION OF SOLIDS. [BOOK I.

between guides in a direction parallel to the exterior troughs, by
means of a milled-headed screw attached to the top of the table.
In this trough was placed the bar, us, whose expansion was to
be measured, bearing at one end, R, against a frame which car-
1 the object-glass, o, of the microscope, E, and at the other
against a moveable frame carrying the object-glass, o', of the mi-
crometer microscope. T and T' represent portions of the tubes
of the microscopes, E and E'. At the commencement of the ex-
peri ment the troughs were all filled with melting ice, and at the
expiration of about a quarter of an hour; which was found suffi-
cient to reduce the bars to the length corresponding to o° Cent.,
the marks m, rri were brought to the centre of the parallel wires,
in the fields of the microscopes, E, E'. The ice was now removed
from the central trough, which was filled with hot water, and
lamps, the handles of which are represented projecting under the
bar RS, were lighted under it, which speedily brought the water
to the boiling point, and maintained it at that temperature until
the bar showed, by ceasing to expand, that it had also attained
the same temperature. During the progress of the experiment
the microscope E was carefully watched, to ascertain if any motion
took place at that extremity of the bar, and to correct it by
means of the screw, in order that the whole amount of the ex-
pansion might be rendered sensible on the moveable frame at the
end s ; the exterior troughs were meanwhile kept full of melting
ice, to preserve unchanged the distances of the eye-pieces, and
also of the marks, from one another. These precautions having
been observed, the turns and parts of a turn of the micrometer
screw, necessary to bring the wires of the micrometer microscope
to their original position with respect to the mark, gave, by an
easy computation, the displacements of the centre of its object-
glass, that is, the amount of expansion of the bar RS. Let a
(Fig. n) represent the mark, o the centre of the object-glass,
and c the middle point of the image of a, at the beginning of the
experiment. Now suppose the centre of the object-glass trans-
ferred to p1 the middle point of the image will be transferred to
0, and the parallel wires must be moved through a space ce to
bring them to their original position with respect to the image
of a, and we are required from ce to compute op. Draw through
o bd parallel to ae, then ce = cd + de = cd + op ; but cd is the image

CHAP. I.]

LINEAR DILATATION OF SOI

of ab = op, formed by the object-glass, \-cd-m. op, m being the
ratio of the image to the object, a ratio easily determined by

periment ; hence ce = ( i + m) op and op

i -r- m

The following Table contains the results of the experiment*
made with this apparatus.

TABLE of Expansions of Metals, fr< iments made in -1

1785-.

Description of Rods.

•hit ions and
Parts ..f th.- Mi-
cronu-UT for the
Expansion of 5
Feet by 1 8o3.

Actual Kx;
in Parts of an hie-
on 5 Feet by 1 80°

Length of a Rod
at 212°, whose
Length at 3 2°= i.

Standard brass scale, .

(Supposed to be Ham-
burgh plate bra.— . --l.-n^th
3.56* bet It» -x pen-
sion -was measuml l.y
25.47 revolutions, there-
.1 iiv»- tVi-t would
be measured by 35.69.)

!i<h plate IHMSS, in
form of a rod, -length

35-69
36.41

O.I 1 1 323

o. 1 1 3 c68

i.ooi 855 4
i.ooi 892 8

i>h plate brass, in
form of a trough, —
I'-nu-th iiv.- feet, . . .
Steel rod, — length five
.......

3645
22.02

j jwt

0.113693
0.068 684

1.001 8949
I.OOI 144 7

Cast iron pri-iiK-k-ngth
five feet

21.34

0.066 c6?

i.ooi 1094

Glass tube,— five l
1 glass rod,-length
3.3~

"4-93

I c.C4

0.046 569

O.O4.8 472

1.000776 I

1.000807 8

msion measured
livi_.4^) r.-v..luti •!>.:
fore that of five f.vt w..ul.l
be measured by 15.54.)

* In Mr. Kamsden'sapparatus, m equalled
5.4. therefore (1 • m), whi.li is the mea-
sure of th.- multiplyin.1 jwwCT of the appa-

ratos, = 4.4 ; hence op = , and con-

«t amount of expulsion which could be

to the least value of «- capable of being

abHTPtl an.! BMMMtd »-v tli.- n.i.-r. in, t. i .

tionsof

tli.' ini.T.iiiu-t.TM n-« :i.|\an.-. .Illn iHrtOM

of the head of the scraw, Uaptrtofa

too

IkxM, vol. K

28 LINEAR DILATATION OF SOLIDS. [BOOK 1.

24. MM. Lavoisier and Laplace's Method. — We proceed now
to explain the construction of the apparatus employed by MM.
Lavoisier and Laplace in their investigations.

M, M', N, N' (Fig. n), represent four piers of solid masonry,
each about two feet by one in its horizontal section, and five feet
in height. I Between these lay the trough, GH, destined to contain
the bar to be examined, under which was placed a furnace built
of bricks, to raise the water or fixed oil surrounding the bar to the
requisite temperature. The bar abutted at one end against a
vertical glass rod FF, maintained in a rigidly fixed position by
its connexion with strong iron bars TT, firmly bedded in the
piers. The bar rested on rollers, gg, fixed at the extremity of
glass stirrups, ff, and at the other end, L, acted on the arm of a
lever, turning on the axis, c, whose other arm gave motion to a
telescope six feet in length, directed to a graduated staff at the
distance of 100 toises. The vertical bar, FF, being supposed to
be absolutely fixed, and the system of levers, LC, L'C, inflexible,
the whole expansion of the bar was represented by the angular
movement of the telescope, od, and the proportion of the several
parts being such that an expansion of the unit of length in the
bar caused the cross wires of the telescope to traverse 744 such
units on the staff, the apparatus appeared capable of estimating
changes of length equal to i -r- 744th part of the smallest di-
vision legible on the staff.*

The results of MM. Lavoisier and Laplace's experiments are
contained in the following Table :

revolution could be estimated, it follows i

the th part of the total length of

that the effect of the micrometer was the 2,000,000

i the bar.

same as if a scale divided into thsofan

7127 In fact in this case the image of the

inch was placed in the focus of the eye- 8taff in the focus of the eye-piece formed a

piece ; and as the divisions of such a scale fineiy graduated scale which was traversed

would be distinctly observable with an by the cross wire. As the staff was di-

eye-piece of sufficient power, it follows that y^d into ]ineS) each line being the twelfth

the least value of op capable of being ob- part of a French inch} and placed at the

served and measured was the th distance of 600 feet, the actual value of

7127x4.4 ,

i each division of its image was about th

= th of an inch. The bars whose 100

3 135°-8 ,

rxj.ansion was examined being in general of a line, or th of a French inch, =

five feet in length, thi> minimum value ,

equalled 0.00000053, or a little more than 7776th °f an EnSlish inch- And sincc a

CHAP. I.]

LINEAR DILATATION OF SOLIDS.

29

TABLE of linear Dilatation of Glass and Metals, from Experiments
made in 1782 by MM. Laplace and Lavouier*.

Name of Substance.

Length at i oo' C.
of a Rod whoM
Length at
o9 = i .0000000.

Dilatation from o'
to i oo 'expressed
in fractional Parts
Ix-ngthato .

I.OOO 890 89

• I i 22

Tube of glass without lead,

I.OOO 8?C 72

' I IJ.2

Do. do.

i.ooo 807 60

I I I A.

Do do

I.OOO OI7 ? I

I OOO

i .000 8 1 1 66

• I 2 l,S

i.ooo 87 1 oo

I I -17

,OOj 722 44

. * »4/
• c8i

Do

ooi 71222

• c8j.

Brass,

.001 866 71

• >°T
••'- C 1 C

Do

.001 889 71

• j jj

' C2Q

.001 220 45

• >^y

•

Do. (drawn),

.OOI 23 C O4.

'y
— 812

.OOI O78 7C

-^ O27

Do. do.

.OOI O7Q c6

• 026

. tempered yellow (annealed at

^ ), •

w/y j^

.OOI 230 c6

. y*^
— 807

Lead,

.002 848 36

— ^?I

Tin (from East Indies)

.OOI Q37 6?

— ci6

* y j i ^j

.002 172 98

. >iu
-i- 4.62

.OOI QOQ 74.

— ?24

ooi 908 68

* ?24.

Gold (de depart.),

i. ooi 46606

• ^*T
— 682

Gold (standard of Paris, not annealed),
'J ( do. annealed), . .
Plutina (according to Borda), ....

1.001551 55
i. ooi 513
1.00085^

4-

-r-
+

25. M. Pouillefs Method. — We next proceed to notice an in-
strument, d« .-ii/ncd, as the preceding, to measure diivrtly the

motion of a line at the end of the expanding

bar caiiMMl th<- cross win- to truvrrx- 744
divWona of the image, = 7.44 line*, it fol-
lows that the mu//i/'///im; |*»wer of the
•yrtem of levers was equal to 7.4
corresponding quantity in Mr. Raratden't
api*ratu» was, as «,• li.iv,- S.-.MI, 4.4. Th.-

motion of the cross wire over one division
of the scale corresponded to an expansion

of -— thofaline = -^-th

100x7.44 744 Sl'iS

! rench inch, » — ^- th of an English

in, I,. TI.i-ON.i-. ||,. -m!,li.M.,..antitx «l,i,l.
BMBfbSMMMM* 01 ttstpMt*! M,,,-

Biot, Trait* de Physique, vol. i. p. 158.

30 LINEAR DILATATION OF SOLIDS. [BOOK I.

linear expansion of solid bodies, invented by M. Pouillet, which
possesses some considerable advantages, particularly that of ena-
bling us to estimate the expansion of bars raised to very high
temperatures, which is impossible by either of the methods pre-
viously described. M. Pouillet's apparatus* consists of a solid
plutc of metal, /(Figs. 12, 13), on which is placed a radius, ob,
turning on the centre, 0, and traversing a graduated arc, vv, whose
divisions are read off by a microscope, xy. This radius carries a
telescope, g, of short focal length, fixed at right angles to its direc-
tion, and a similar telescope, A, is fixed to the plate itself, allowing
the radius to traverse under it. The bar under examination
being placed in the copper trough (Fig. 14) furnished with plates,
>//, n, of parallel glass, through which its extremities may be seen,
if one extremity, n, be kept opposite the fixed telescope, 7t, and the
moveable telescope, g, be directed to the extremity, m, at the com-
mencement of the experiment, then any expansion which the bar
undergoes, by the elevation of its temperature, may be estimated
by the arc through which the radius must be turned to bring the
telescope, </, to bear on the other extremity, m, in its new position,
the distance of the radius from the bar being accurately known.
For very high temperatures the bar may be placed in a furnace,
and when raised to the temperature required, apertures may be
opened in the furnace walls, giving a view of the ends of the bar,
and allowing its expansion to be measured in the manner de-
scribed, f

positions with respect to the distance of the paratus, therefore, was inferior to that of

staff and its graduation ; had the staff MM. Lavoisier and Laplace's, its measnr-

been divided into half lines, or placed at ing power appears to have been far more

the distance of 200 toises = 1200 feet from sensitive, as well as more accurate,
the object-glass of the telescope, the value * Elemens de Physique, vol. i. p. 234

of each division of the image would have (fourth edition).

been — th of a line, and the smallest ex- t In the apparatus, as employed by M.

200 Pouillet, the ratio ob:om (Fig. 13), was
pansion capable of measurement would have , ..

f about 3:1, and as the microscope was ca-

been -th of a French inch : but MM. . i ,

17856 pable of reading a motion of — th of a

Lavoisier and Laplace state, that on re- ....

millimetre at &, the apparatus could anprc-
moving the staff to that distance, the x

.listinctneu of the image was sensibly im- ciate an expansion in the bar of — th of

paired, owing to local currents in the air, i

a millimetre, or about th part of an

and irregular refraction. Although the 50,000

multiplying power of Mr. Ramsden's ap- mcn>

CHAP. I.] LINEAR DILATATION OF SOLIDS. 31

26. Mr. Daw. // '/ M-/._In the Philosophical Transactions
for the years 1830, 1831, is contained an account of an instru-
ment called " a register pyrometer," for the measurement of the
linear dilatation of solids, by Mr. Daniell. This instrument, repre-
sented in Figs. 16, 17, on a scale of one-half the full size, consists
of two parts, of which one is called by the author the register, the
other the scale. The former (Fig. 16) consists of a solid piece of
•k-lead earthenware, eight inches long, and seven-tenths of an
inch in width and depth, cut out of a common black-lead crucible.
In this a hole is drilled, about three-tenths of an inch in diameter,
to the depth of seven inches and a half. The upper end of

ut half through for the length of about six-tenths of an
inch. A rod of the material whose expansion is to be incasu.

inches and a half long, is dropped into the hole in the bar
of black-lead, and presses at one end against its extremity; a
piece of well baked porcelain, of the same diameter, and an ineh
and a half long, is placed against its upper end, and serves as an
index of the expansion of the metal rod. This index is confined
in its place by a platina ring and a wedge of porcelain, which so
far constrain its motion as to admit of its being pushed out-
wardly by the expansion of the metal bar, but retain it in that

>n on the contraction of the latter.

The scale (Fig. 17) is constructed of two rules of brass, ac-
curately joined together at a right angle by their edges, and iit-
tinir square upon two sides of the black-lead bar, and of about
half its length. At one end of this double rule a small plate of
brass, X% projects at a right angle, which plate, when the two
sides of the former are applied to the two sides urister, is

i upon the shoulder formed b\ h cut away

ti upper end, and the whole may be then firmly adjusted to

.tek-lead bar l>v three planes of contact.
( )n tin- outside of this frame another brass rule, gh, is firmly

down, which carries at ite c>.
round the c.-utre, a. When the scale is appln

•er acts on a pin. in of

v half an inch from the ceil-

.-in, win' ^th, tra-

32 LINEAR DILATATION OF SOLIDS. [BOOK I.

-os a graduated arc divided into degrees and thirds, and read
off by a vernier on the radius to minutes.

This instrument is thus used. The metallic rod is introduced
into the hole in the register at the temperature of the surrounding
medium, and the porcelain index pressed home against it, and
secured in its place ; the scale is next attached to the register in
a determined position, by means of a guide, k, which rests on the
shoulder, /, and the indication of the radius on the arc noted, or
brought by means of a spring to the zero of the graduation.
The scale is then removed, and the register exposed to the
temperature to be measured. After it has been withdrawn and
allowed to cool, the porcelain index retains the position corres-
ponding to the maximum expansion of the rod, and the scale
being again applied to the register in exactly the same position
as before, the arc through which the radius must be moved to
bring the point p in the arm of the lever to bear against the index,
measures the quantity by which the latter has been protruded.
This quantity is clearly the excess of the expansion of the metallic
rod over the black lead envelope, or rather it is that excess dimi-
nished by the contraction of the index due to cooling from the
higher temperature to that of the surrounding medium ; the total
quantity is, however, so small in all cases, that this correction of
it is quite inappreciable.

On comparing the apparent expansion of platina and iron rods
in this apparatus by immersing the register in boiling mercury, or
in boiling water, with their real expansion, as determined by MM.
Dulong and Petit, Mr. Daniell obtained the expansion of the
black-lead envelope ; he found this to vary in different specimens,
but to be perfectly constant for the same change of temperature
in the same piece.

The expansion of the envelope having been thus determined,
it was only necessary to add it to the apparent expansion of any
metallic rod operated on, to obtain the real expansion of the latter.
By this means Mr. Daniell obtained the following table of the
expansion of the metals enumerated in the first column, from the
temperature of the surrounding medium, 62° F., to those of
boiling water and boiling mercury.

CHAP. I.]

LINEAR DILATATION OF SOLIDS.

i B ! oseLengtJi at 62° F. w i.oooooo.

Substance observed.

'; .it :i : 1 .
.^eo{ 150 ).

Length at (»
(Change of 600').

Lnfthti ivim i.r
Fusion.

k lead W;

are, .
Plat ina, ...

I.OOO 244

i.ooo 735

I OOO 7 3 C

1.000703
1.002 995

J OO2 OQC

(I ooo 02^) m&T

Iron (wrought), .

I jj
1.000984

i.ooo 80?

i.wwa yy^

1.004483

I.OO3 <J-i?

l>ut not fused.)
(1.018 378 to

lit Of

cast iron.)
1.016 ?8o

Gold,

i.ooi 025

I OO4. 2?8

i.ooi 4.30

I. OO6 147

I.O2J. 576

i.ooi 626

i. 006 886

i. 020 640

Zinc

I OO2 480

i 008 527

I OI ""

Lead,

I.OO2 121

I .OOQ O72

I.OOI 472

i.oo^ 708

K» •

Bronze, Tin, {-, . .
Type metal, . . .

i.ooi 787
i.ooi 541
i.ooi 696
i.ooi 696

1.007 207
1.007053

1.02 I S4I

1.016 336
1.003 7?6
1.004830

27. Mr. A 'In? 8 Method. — Mr. Adie* read a papi-r in April,
1835, before the Royal Society of Edinburgh, on the cxjuir
of different kinds of stone from increase of trni[>rniture. Hi- py-
rometer, which is admirably suited fur the examination ofsiu-h
;ances as are aflirted by moisture, consisted of a
•vlinder, about t\v«» inrhc- in diamncr. and twentj-M^

• inches lou*:, whieli contained the rod whose expan-
sion was to be measured. This cylinder was !• <1 by a
•n-tiijht case, thmuijh wliirli a current <•!' -train was passed^

.irpo.-f ••!' rai.-!HLr the temperature of !:.
contained rod. Y\g. 1 8 represents a horizontal, an<; i
1 secti-.n of the eylind.-r and case ; BBS is the

vimluw <>f plate glass, giving a view of th-
of the rod c. Ti lestcd on a support which

was capable of 1 1 in ln-i«_'ht by means of a s

the bottom of the cylinder, and was steadi.d

he Royal S- p. 354.

I

I.IXKAR DILATATION OF SOLIDS. [BOOK I.

ii-s l>v a couple of springs and friction rollers. Two
silver studs \\viv fixed in tin1 rod, at the exact distance of twenty-
three iiulus at the ordinary temperature. The cylinder and
case were secured to a vertical beam of well-seasoned oak, to
which were attached two microscopes E, E', having their axes
horizontal, directed towards the studs in the bar. The lower
microscope enabled the observer to keep the lower stud perfectly

ionary, and the upper one, by means of a micrometer, measured
the expansion of the bar. The oak beam to which the micro-
scopes were attached was protected by a screen of polished metal
from the radiation of the heated case ; and as the expansion of the
wood of which it was composed was ascertained, by direct obser-
vation, to amount to only .000062 of its length for a change of
1 80° F., the distance between the microscopes may be assumed
to have continued invariable. A current of steam being passed
through the case, regulated in quantity by a valve on the supply-
pipe, a constant temperature could be maintained in the inner cy-
linder for any length of time ; and when the rod ceased to in-
crease in length its expansion was measured. In Mr. Adie's
experiments, the temperature to which he raised the rods was
generally about 207° or 208° F., and it required about four hours
to bring a rod, whose section was a square from half an inch to
an inch on its side, to this temperature from 50° F., the ordinary
temperature at the time of the experiments. From the amount
of the expansion for the observed change of temperature, about
157° F., Mr. Adie calculated the following table of expansions
for i8o°F.

In the case of greenstone and some descriptions of marble,
the effect of moisture was to increase the amount of expansion ;
in other instances no effect of this kind was perceptible. Mr.
Adie also found that in white Sicilian marble a permanent in-
crease in length was produced every time that .its temperature
was raised, the amount of increase diminishing each time.

CHAP. I.]

LINEAR DILATATION OF SOLI1'-

TABLE of Expansion of Stone,

D.rinuilsof an

Inrh
: J So F.

Length at 212*

if a i:<»| \ih-.M-
Length at 32'

= 1 .0000000.

ObMtntioM.

i. K u-iit.

•033 004 3

1.00 1 4349

\Vlu-n the rod ,

dmoremois-

tuiv it t-xpa:.

more.

•iliuii white
marUf

\ -°32 539 2
L .025 394 6

i .00 1 414 7
1.001 104 i

From first

: \vlK-M in
Mi-an ex-

ju-riiiu-nts \\

dry.

r .0274344

i.ooi 192 8

From fir>:

3. Carrara Marble,

J

ment when moist.

.0150405

i .000 653 9

i Of tWO C'.\

rimentswhendrj.

4. Sandstone from

lime rock of

ithquar-

.027 ooo 3

i.ooi 174 *

i>f four •';

5. Cast iron from

*m j wvy j

/ i J

a rod cut from

a bar ca-t two

inchr> square, .

.0263755

i.ooi 146 7

Mean of two i-

:..I1 from

a rod oast hull'

an iin-li

.025 349 S

I.OOI 102 2

7. Slate iron:

rhvn tjuarry,

\\ • . ...

.02^ 86? o

i.ooi 037 6

8. Peterhead

^~ j ^^ j j

{.022 041 6

«J /

I.OOC

. . .

.020 fofi (">

1.0008968

rinu-nt- M

ith pave-

^

HP . .

.020

1.0008985

ditto,

10. Cuitluifss :

J

4

.020 578 8

1.0008947

Mean.", t

.OlH 604. \

1.000808 o

'jrcy

T J

t j

.OlS

i.ooo 7894

.012

I.OOO 550 2

litto,

I INKAR DILATATION OF SOLIDS,

[BOOK i.

Name of Substance.

ils of an
Imh on 23

l.< ii-th at 212"
! \\hnsr

I.niutli at 32°

= I.OOOOOOO.

OWrv:itions.

14. Fire brick,. . .

-on 3334

1.000492 8

Mean of two expe-
riments when dry.

^ talk of a Dutch
occo pipe, . .

.0105177

1.0004573

Mean of three ditto.

1 6. Round rod of

•dgwood ware

:ios long)

....

i.ooo 452 9

Mean of two ditto.

17. Black marble

from Gal way, 1.

•01023;-}.

1.000445 2

Mean of three ditto.

rod

of Gal way bi

mar 1>K'. contain-

ing more fossils.

and softer than

I OOO 4.7 Q 3

w T/ 7 J

28. Remarks on the preceding Methods. — These methods of ex-
menting are liable, it will be seen, to two classes of errors,
one arising from inaccuracies in the measurement of the amount
of expansion, the other from similar inaccuracies in the determi-
nation of the corresponding changes of temperature. In Rams-
den's method, as we have remarked, the limits of the former class
of errors may be determined, but in the others, though doubtless
Hnall, they cannot be ascertained with accuracy. In all these
methods, however, there are only three or four temperatures
which can bo determined with rigid accuracy, namely, those of
melting ice and of boiling water, oil, and mercury; and accord-
ingly, though a few intermediate temperatures have been sought
to bo determined with extraordinary care, yet, owing to the dif-
ficulty of keeping all the parts of the bath at the same tempcni-
, and maintaining the whole at a constant temperature for a
'li «>i' rime sufficient to insure the bar immersed in it having
acquired the same, we are hardly justified in considering such ob-
;nd the corresponding expansions, as more
than approximations to the truth.

M Bordcts comp<n it,,, .I/,-//,,,,/. — Before concluding thLs
part of our subject, we will describe u method by which the linear

CHAP. I.] CUBICAL DILATATION OF SOLIDS. 37

n -i<»n of bodies may be determined by comparison with some
. of known expansion. This method was first employed by
M. 15,>rda to ascertain the expansion of the measuring rods made
<»f in the survey for determining the length of an arc of the
Mian, and lias been since applied to the determination of
linear expansions generally by MM. Dulong and Petit. The
methud is this. A bar AB (Fig. 20) of the substance to be
amined is placed on a similar bar CD, whose expansion is known,
and is I irmly secured to it at one end A, in a fixed line ef, while
to move on it at the other in a direction perpendicular
At the end B it is bevelled off for a short distance to a
sharp edge oj>, and after the two bars have been kept in melting
For a sufficient length of time to bring them both to the tem-
;ure of o° C., a line abed is drawn parallel to ef. The bars
:hen placed in boiling water, and as soon as they have ce;
•;pand, the point c on the lower bar is marked, to which the
line ulic on the upper bar, supposed more expansible, has ad-
vanced. Let the distance cc at o° be a, at the temperature
huiling water it will be = a(i + Sr), $T being the coeiH-
• of linear expansion of the bar CD for 7'°; but this dist;

is the excess of the expansion of the length ea of the bar
.1 11, over the same length of C'/>; call this length at o° /, an

"cifiit of linear expansion of the bar All; then we have

$T') - l(i + $T) = a(\ + Sr), or S; = $T+ j(i + 8r), which g

the expansion of the bar AB in terms of that of CD*
30. M>tl«»l < * nitty the cubical Dilatation <>f '/'/.

cpanrion of solid hudics having hren determined hv

..f tin- preceding method.-, their cubical rxpaiiHon mav he

...in it hv calculation, a- will be shown 1. : hut

ruined by direct experiment, the cu-

n of mercury being lii>t known. Th-- nu-th.-d hv

which the cxpan.-ion nf r ha- been determined will be

i ; ue \\ ill, meantime, sii|>|».
R how, with its assistance, the cubical dilatation

nr- in tlii

38 CUBICAL DILATATION OF SOLIDS. [BOOK I.

. first, the cubical dilatation oi' glass is determined as fol-
lows. A cylindrical vessel of this material is constructed of the
form represented in Fig. 21, terminating in a line capillary tube.
The :illed with carefully purified mercury, which is then

boiled for a considerable length of time, until all air and moisture
mplctely expelled. It is next surrounded with melt-
: he end being kept immersed in mercury, until the whole
mass has assumed the temperature of o°. It is then removed
from the ice, and placed, as represented in Fig. 22, in a vessel
obtaining a small quantity of water, whose temperature is gra-
dually raised to the boiling point, so that the glass cylinder is

Dually enveloped in steam of the temperature T7, at which
water boils under the barometric pressure existing at the time of
the experiment. During this process the mercury and glass are
gradually expanding, and the portion of the former which is ex-
pelled is collected in a small capsule. When they have both
attained the temperature of the surrounding steam, and have
consequently ceased to expand, the vessel is removed, and the

-lit of the mercury remaining in it, as well as of the quan-
tity expelled, is carefully ascertained. We have now all the
data necessary for the determination of the cubical expansion of
the glass vessel from o° to T°. For let W be the sum of the
weights of the mercury remaining in the vessel, and of that col-
lected in the capsule, w the weight of the latter alone; then \V
is the weight of the mercury which filled the vessel at o°, and

W .
if D be its density at that temperature, -=j is the volume of the

mercury, and consequently of the vessel, at o°. The volume
of the latter, therefore, at T, is -y-(i +8r), if Sr be the co-
efficient of cubical dilatation of glass for T°. It is clear also
that W - w is the weight of mercury which, at the temperature
'/', fills the expanded vessel; the volume of this mass at o°, there-
fore, is — j- — , and at Tit is — j- — (i + A7.), Ar representing

the coefficient of cubical expansion of mercury for 7'°. Kqua-
the expressions of those quantities, namely, of the volume of
the vessel at 1\ and of the volume of the mercury which filly it
;a that temperature, we have

CHAP. T.] CUBICAL DILATATION OF SOLIDS. 39

and there;

3 1 . M^cthod of dct ifa —

The expansion of glass being thus ascertained, the expansion of
i i-i ui is determined as follows. Let a bar of iron, whose weight
and density at o° are known, be enclosed in a glass ve.-sel shaped

i the last experiment, and the vessel then filled with mercury,
and boiled a- before. Let it be cooled down to o°, and the incr-
eurv which is expelled when its temperature is subsequently

d to 7*°, the temperature of the vapour of boiling water,
collected and weighed. Let the weight of that which remains

dso ascertained. Let 1\ be the sum of those weight-.
the weight of mercury expelled, I) the density of mercury at o°,
u- and // the weight and density at o° of the iron, A^ §„ S?, the
coefficients of cubical expansion of mercury, glass, and iron for
T .

Then the mercury, whose weight is IV '- w, and accordingly

U -w
o° = — r. — , and the mass of iron whose volume at

the same temperature equals — on being raised to 7°, fill the

/ W w'\

toae volume at o° was fy- 4- — J, and which at '/' be-

*\
cornea

f]V ,r\ ( \

( T- -J- — r- ( I + CT } : thereloFe we have
\j) </ J \ WJ'

11 , i-(i+Ar)4-^- (i +«;)

rC+^J ",--

• nf the metals which
by mercury i in«- me-

to tln-ir imm.-i don in tin- nirivurv, tlir\
in it- aeti«.n by • tli.-m willi u thin lilt

)X' '!•'• () 'ii of such metals ma \

LAWS OF DILATATION OF SOLIDS.

[BOOK i.

o >input<*d from the linear, ami this latter may be determined by
.\v method described in (29), from the linear cxpan-
»f iron, previously computed from its cubical expansion.
The following Table contains the results of MM. Dulong and
I' Ys experiments on the cubical dilatation of glass and some
metals.

TABLE of the cubical Dilatation of Glass, §c.*

Substance.

Mean Coefficient of Dilatation for i°
between o3 and ioo\

Mean Coefficient for i° between o°
and 300°.

In vulgar
Fractions.

In Decimals.

In vulgar
Fractions.

In Decimals.

Glass, . .
Iron, . . .
Copper, .
Platina, .

I _ 38700
I — 282OO
I — 19400
I —37700

O.OOOO25 839
0.000035 461
o.ooo 05 1 546

0.000026525

I .4. 32900
I -i- 22700
I _i- 17700
I _i_ 36300

0.000030 395
0.000044052
0.000056497
0.000027 548

MM. Dulong and Petit also give, as the value of the mean co-
efficient of glass for i° between o° and 200°, in vulgar fractions,
i -f- 36300, or in decimals, 0.000027 54^-

M. I. Pierref has since found, by the same method, that the
mean coefficient of the cubical dilatation of glass for i° between
o° and 100° varies in different specimens from 0.000019026 to
0.000026025.

32. Laws of Dilatation of solid Bodies. — Having thus briefly
described the principal methods of determining by experiment
the amount of dilatation of solid bodies, we will proceed next to
state the general laws derived from them.

LAW I. — All solid bodies, which do not undergo any physical
change or loss of substance by the action of heat, increase in volume
ii-itk increase of temperature, and on being restored to their initial
temperature resume accurately their original volume.

The case of clay balls, which contract on being exposed to a
very high temperature, and do not return to their original volume,

* Annales de Chimie et de Physique, tome vii. p. 138.
t Id. tome xv. p. 335 (3me Seric).

CHAP. I.] LAWS OF DILATATION OF SOLIDS. 4!

offers only an apparent exception to this rule. For it has been
proved that the diminution of volume in this instance arises from
an actual loss of substance, owing to the liberation of water,
which is held in such intimate union by the alumina of the clay,
that even a red heat is insufficient altogether to expel it.

\\ will see that this law holds also in the case of liquid and
ous bodies, a few of the former, when near the temperature
at which they undergo a change of state, being excepted.

A singular anomaly occurs in the case of Rose's fusible metal,
— an alloy consisting of two parts bismuth, one lead, and one tin,
which molts at 75° R. M. Erman* has found that the melted
,1 contracts, on cooling, according to the general analogy,
until it solidifies at the temperature of 75°; after this it still con-
tinues to contract until it attains to 55°, from which point to 35°,
on the contrary, it expands, and after that contracts again, and
continues to do so to the lowest temperatures. On tracing a
curve whose ordinates r-hall represent the increments of volume,
in parts of the original volume at o°, and abscissae the degrees on
Amur's scale, the course of the curve from the origin to the
abscissa, 35°, approaches nearly to a right line, showing that
here the change of volume is nearly proportional to the tern;
ture: at 35° there is a maximum ordinate: from 35° to 55° the
o descends towards the axis of the absciss.-e, more rapidly at
. and more slowly as it approaches the latter point, when tin;
ordinate has a minimum value : on passing 55° the ordinal.
crease, at first slowly, then more rapidly up to the abscissa cor-
iitv-liiili degree, the melting point of the
il: from 75° to 80° the rate of increase is still considerable,
after 80° it resumes a rate of pro^ros which appears i
rously the same as that which was observed before tin- anomalous
changes occurring between 35° and 75°; so that in this metal
.ige of volume i- •/. j>. proportional to tl: < of temp

. with the exception «.f the part of tin- .-rale between the points
above-ni' m an-malous oscillation occurs. I

to be remarked, that the M.lume at tin- melting point, 75 \ i
same as that at the point of relati\ nn, 35°, so that

' Annnlo* •!•• ( hiuii. it p. 197.

G

42 LAWS OF DILATATION OF SOLIDS. [BOOK I.

horizontal tangent to the curve at the latter point cuts the ascend-
ing branch of the curve, at the point whose abscissa is 75°. It
is probable that this anomaly is connected with some change
which takes place in the arrangement of the molecules of the
metal consequent on the change from the liquid to the solid state,
and that it is analogous to a similar phenomenon in the case of
water, with this difference, that in the latter substance the ano-
maly begins to exhibit itself before the change takes place, but
in the fusible metal not until afterwards.

33. LAW II. — Homogeneous uncrystallized solid bodies expand
uniformly in all their dimensions, so as to preserve similarity of
ji.jure.

By means of this law we are enabled to establish a relation
between the cubical, superficial, and linear expansions of a body,
that is, the expansion which a body undergoes in volume, in the
area of any surface, and in the length of any of its edges or
sides.

Let V represent the volume of a body at any temperature, ft
its coefficient of cubical expansion referred to that temperature
for tQy so that ft V expresses its expansion for the given change
of temperature. Similarly let S be the area of any surface at the
original temperature, and ft' the coefficient of superficial expan-
sion, L the length of any edge of the body, and ft" the coefficient
of linear expansion, all these coefficients referring to the same
original temperature and same change (2°), so that V(i + ft),
S(i +ft'), L(\ + &")» wiH express what F, S, and L become after
expansion. Then as the volumes of similar bodies vary as the cubes
of their homologous sides, we have F(i + ft) : V: : L8(i+ ft")3 : Z3,
and v ft = 3ft" + 3ft"2 + ft"3 ; whence if ft" be so small that we may
neglect its square and higher powers, as is the case with most
solid bodies, even for considerable changes of temperature, we
have

&=3&"-

In like manner, as similar surfaces vary as the squares of their
homologous sides, we have S(i + ft'): S:: L2(i + ft")2: Z2, and
ft' = 2Vt+ ft"2, or, neglecting ft"2,

ft' = 2ft" and consequently ft = - ft'.

CHAP. I.] LAWS OF DILATATION OF SOLIDS. 43

K«»r any change of temperature, therefore, the corresponding
icients of cubical, superficial, and linear expansion are in the
3:2:1, if the last mentioned coefficient be so small that its
square and higher powers may be neglected.

A hollow body, it may be remarked, expands in all its di-
mensions, exactly as a solid body of the same volume and n:
rial. For conceive a sphere composed of successive concent rie
shells, such a sphere must expand exactly as a solid one, and
therefore every shell separately must expand as if the others
• away.

34. LAW III. — Some crystallized bodies do not expand uniformly
in nil ifif' let' (//<• net i<>n of heat.

Change of temperature in such bodies is accompanied both
by a change in their optical properties, and also in the di-
mensions of the solid angles formed by the faces of their cry-
M. Fresnel* appears to have been the first who discovered this
property of crystals, to which he was led by observing that the
double refracting power of sulphate of lime was sensibly dimi-
n'^hed by a rise of temperature. He subsequently proved by a
very simple experiment the unequal dilatation of this crystal in
different directions. Having cut two very thin plates from a crystal
of sulphate of lime, parallel to its prismatic axis, that is, to the line
i the acute angle formed by its optical axes, he placed
one upon the other with an intermediate layer of cement, in such
>sition that the direction of the axis of one plate form

with that of the other. The temperature of the

plates was then raised sufficiently to melt the cement, alter which

they were allowed to cool. When, in the process of cooling, the

••nt had become sufficiently hard to prevent one plate from

sliding <>n t!.' :ln- unequal contraction of the plates caused

them to warp or bend, in such a manner that each plate formed

a C<M Erection in which it was most dilatable,

n perpendicular to its a\i>, while it formed

in the direction at right angles to this.

iinent* on ihecha
106 on their unequal <• ; in different • .s by

* Bull.-im .l-la \ ,823.

44 LAWS OF DILATATION OF SOLIDS. [BOOK I.

heat, were made by M. Mitscherlich.* Measuring the angles of
crystals of carbonate of lime by the goniometer, he found that the
obtuse angles of the edges of the rhombohedron diminished by 8'.5
on a change of temperature from o° to 100° C., and that the acute
angles of the other edges increased. Hence it followed that the
smaller axis of the rhombohedron was more elongated than the
other diagonals, and that the form of the crystal consequently ap-
proached more nearly to a cube. From the alteration above men-
tioned, produced in the angles of crystals of carbonate of lime, it
follows, that, supposing the dilatation in the direction perpendi-
cular to its axis to be zero, its cubical dilatation should still
exceed that of glass by about one-half. Experiment, however,
proves, on the contrary, that it is less, from which we are forced
to conclude, that while, on rise of temperature, this crystal dilates,
according to the general analogy, in the direction of its axis, it
actually contracts in the direction perpendicular to this. In con-
firmation of this conclusion, M. Mitscherlich records, that on mea-
suring at different temperatures, by means of a spherometer, the
thickness of a plate of calcareous spar, cut parallel to its axis, lie
obtained a result similar to the preceding. From this it is proba-
ble that sulphate of lime presents an analogous phenomenon, but
in the inverse direction, namely, that the action of heat produces
in its crystals a contraction in the direction of the axis, combined
with a dilatation in the perpendicular directions.

M. Mitscherlich f gives the following as the results of his in-
vestigations into the action of heat on crystals, a detailed account
of which he has published in the Transactions of the Academy of
Berlin for 18254

(i). Crystals belonging to the regular system, and which ac-
cordingly do not possess the property of double refraction, dilate
uniformly in all directions, and exhibit no alteration in the value
of their angles on rise of temperature.

(2). Crystals whose primitive form is a rhombohedron or hex-

Annales de Chimic ot tie Physique, xxxii. p. in.

.lanvi.-r 4. 1834. f Ami also in 1'oggendorff's Annalen,

t l'«»wiulorfl"s Annalen, 1824, No. 5, 1827,1*0.5.
and Ann. <l<- Chiinie ct <!<• I'liyHcnic, tome

CHAP. I.] LAWS OF DILATATION OF SOLIDS. 45

aedral prism, that is, those belonging to the hexagonal system,* are
dilierentlv affected by heat in the direction of the principal axis,
and in the direction of the three secondaries, but in the direction
of the latter they are similarly affected. Thus we have seen that
carbonate of lime expands in the direction of its principal axis,
that is, the line uniting the obtuse solid angles of the rhombohe-
dron,and contracts in the direction of the secondary axes perpen-
dicular to the former.

(3). Crystals whose primitive form is a rectangular or rhom-
boidal octahedron,f or generally all whose double refraction de-
pends on two axes, dilate unequally in all directions.

(4). The dilatation of crystals in different directions is alwavs
•eted with the position of their axes of crystallization, and
as the.-e have a necessary relation to the optical axes, it follows
that their dilatation has a fixed relation to the latter. In general
the shorter axes dilate more than the longer, or dilate alone,
while the latter contract. Hence Mitscherlich concluded that
the tendency of heat is to increase the mutual distance of the
molecules in the direction in which they are most condensed,
and consequently to equalize those distances in different direc-
tions, and so bring the different axes to a state of equality.

35. LAW IV. — Relation between the Expansion of Solids and tlie
<ij>j»irt>nt Expansion of M< /•/•//;•// in (Mass.

i the limits of o° and 100° Cent., the expansion of all
solid bodies is sensibly proportional to the change of teinpera-
, as measured by the mercurial thermometer. In other word-,
<• limits their expulsion tor any change of tempera-
is proportional to the apparent expansion of mercury in glass
-ame change. After passing the limit of 100°, however,
ii of solid bodies is found to iiu-re is<- in a more ra-
pid ratio than tl.eir temperature, the latter being .<til; «1 by
! temperature. .MM. I. av. .i.-ier and Laplace observed
a striking exception to t, the ease of temj-

ir<l >>r rliombohedral system of b <» < MiM yatems

Row- >\aL We mmy as- of Rose. Opt:

sumo that this Uw applies also to the se- be assumed to applx law t.. th- MM!I of

ire system of Rose, whi.-li. iL.ul.ly ..l.li,,.

i \aL

46 LAWS OF DILATATION OF SOLIDS. [BOOK I.

steel, whose rate of expansion diminishes as the temperature in-
creases.* This anomaly appears to be due to the fact that stivl
is partially deprived of its temper by the action of heat, and so
brought gradually nearer to the condition of untempcred steel,
whose dilatabiiity is less than that of tempered. We may take
this opportunity of remarking, that in the process of tempering
steel undergoes a permanent dilatation, varying in amount with
the dimensions and shape of the mass, and the temperature at
which it is suddenly cooled; and hence the violent torsions and
alterations of form which pieces of steel frequently undergo in
tempering.

36. Expression for die Volume, #c., of a Solid in Terms of its
Temperature and Coefficient of Expansion. — It follows, from the
law just stated, that for solid bodies, between the limits o° and
1 00°, the coefficient of dilatation varies with the number of de-
grees expressing the corresponding change of temperature ; for as
the expansion may always be expressed in the form S,Q, where
$t is the coefficient of expansion corresponding to a given number
t of degrees, and Q the volume, surface, or length, and as c^Qva~
ries as t, it follows that St varies as 2, and hence if k expresses
the value of the coefficient of expansion for i°, kt will express
its value for t°. In practice the amount of expansion determined
is almost always that corresponding to the change of temperature
from o° to T° Cent., T° being the temperature of the vapour of
water boiling under the atmospheric pressure existing at the time
of the experiment, or, what is nearly the same thing, the tempe-
rature of the upper stratum of water boiling in a metallic vessel
under that pressure. This temperature is, in many instances, as-
sumed to coincide with the boiling-point of water under the
normal pressure, that is, 100° C., or 212° F. ; but where strict
accuracy is desired, the value of T° should be determined for the
given circumstances of the experiment by the method indicated
in the second chapter of this Book.

The coefficient of expansion usually determined, therefore,
is the fraction of the value at o° C., by which a body expands in
volume, .surface, or length for 710, and the coefficient for i° is

I5iot, Trailc de Physique, tome i. p. 157.

CHAP. I.] LAWS OF DILATATION OF SOLIDS. 47

^th part of this. Hence it' T0 denote the volume at o°, and Vt

the volume at /°, we have Vt= V0(i + /•/), and similarly if Jy be
the volume at t', 17 = V0 0- + ^'0> whence in general

r, i + &

by means of which expression we can compare directly the vo-

lumes at t and t .

\Ve have, in the same way,

St i + k't , Lt i + k"t

/•, k\ /•", the coefficients of cubical, superficial, and linear expan-
sion for i° C. being, as was shown before fjipiu the ratio 3:2:1.
The numerical values of the coefficients k, k', #', which are
generally given in physical treatises, refer, as we have mentioned,
to the volume at o° C. As there is no reason, however, for fixing
upon this volume as the standard, except the facility of deter-
mining the corresponding temperature, the coefficients may be
referred to the volume at any other temperature, and their corres-
ponding numerical values obtained as follows. In the equation

V V l + kt

r'=F"777?

put t - t' r r, then

orFT=F(i+Kr);

if, therefore, we count our degrees from a temperature t'°, and

te them, when counted from this point, by the symbol r,

the volume at t' as the standard, then the « it, as

to this Standard, Ix-ars t«» the eorilieient /•. relenvd to the

volume at o° as stand BMed !>y the equation

-- 7-,.* .- "I" the rnrllii-icntS

i

* If* tx- expressed by a vulgar fraction », c wiU be expressed byasimikr fr a

whow denominator inn • t.

48 LAWS OF DILATATION OF SOLIDS. [BOOK I.

of superficial and linear expansion. It must be borne in mind
that these methods of expressing the volume at one temperature
in terms of the volume at another, only apply between the limits
within which the fourth law is true.

37. Remarks on the Values of the Coefficient of Dilatation of
various Solids. — The coefficient of dilatation of glass varies con-
siderably with its composition. MM. Lavoisier and Laplace
found it to be less in proportion as the glass contained more
lead.* M. Regnault, who has been led to examine this sub-
ject with particular care, has found not only that the dilata-
tion of different kinds of glass varies within very wide limits,
but that the value of the coefficient varies in different pieces
of the same kind, according as they are in the form of tubes,
or have been blown into bulbs of different dimensions, and that
even the dilatation of the same apparatus, between the same li-
mits of temperature, is not always identical. " The differences,"
says M. Regnault, " observable in the dilatation of the same
piece of glass, when in the form of a tube, and when blown into
bulls of different dimensions, do not appear to follow any simple
law. Thus, ordinary white and green glass dilate less in the
form of a ball than in that of a tube. The contrary is true in the
case of Swedish, infusible French glass, and crystal. The same
glass, formed into a ball, appears to dilate more as its diameter is
greater, or perhaps as the thickness of its sides is less. In every
case we see how liable we arc to fall into serious errors, in ex-
periments requiring extreme accuracy, from calculating the dila-
tation of an instrument of glass, by means of the coefficient
obtained even from direct experiments on a tube or ball of the
same material, much more from the linear dilatation of a rod of
the same kind of glass, as has been done by many eminent phy-
sicists.'^

The coefficients of cubical dilatation of glass for i° between
o° and 100° vary, as we have seen (p. 40), according to M. I.
Pierre's experiments, from .00001902610.000026025, so that the
difference between the extreme values exceeds one-fourth of the

* Riot, Traiti: (In Physique, tnnio i. p. 157.

f Ann. do Cliim. et do Phys. 3nie Ser. tome iv. p. 67.

CHAP. I.] DILATATION OF LIQUIDS. 4!

M. K''untult lias also found that different kinds of g
follow different laws in their dilatation, those whose coefficients
of expansion an; smallest increasing less rapidly in the rate of
their dilatation.*

The coefficient of iron also differs very much in different
•linens, thus confirming the result derived from other sources,
the iron of commerce is by no means an identical metal.
same remark applies to brass; in fact, it is to be obser
generally, that unless we are certain that the strictest physical
.lity in composition and molecular arrangement exists be-
11 two bodies, we are not justified in assuming that their co-
onts of expansion possess the same numerical value.

SECT. II. DILATATION OF LIQUIDS.

38. Dej' Between Coefficients of

real Expansion . — As liquids can be experimented on only in solid
id as on a rise of temperature the latter must increase
in volume as well as the former, it is obvious that the expansion
of the liquid in tl >pe, or, as it is called, its appan-n'

will be modified by the expansion of the envelope ii
re proceeding to describe the n I ' dct.-rminin^ by

penmen- msion of liquids, we will point out the relation

ween tip- real expansion of the liquid, that Is,
iae of \..lume due to any rise of temperature, —
, -parent expansion, «,r the increase <>f its volume over that
and the expansion ot' the latter. For this pur-
l«-t us suppoM- the liquid contained in a graduated tube
I bull) alt . and let I

repr< occupied bv the liquid at the teinpeia-

t £°, as *
.her of dr. it fills in the ml

luuir which ii really at that t«-nn

litv of tl n into account. Fur-

0| its coefficient < •• coelli-

102.
II

50 DILATATION OF LIQUIDS. [BOOK I.

cicnt of expansion of the envelope for the same change oftempe-
v. Thou since Vt = V0 (i + &), and Vt = V! (i + //), we

•A-C have also 17= F0(i +0,); therefore

or

The last term of the right hand member of this equation is so
small that it may, in most cases, be neglected, so that we may,
in general, assume

$t = 0t+ kt,

that is, the coefficient of the real expansion of a liquid for a given
change of temperature equals q.p. the coefficient of its apparent ex-
pansion + the coefficient of expansion of the solid envelope for the
same change.

39. MM. Dulong and Petit s Method. — The first method of
ascertaining the expansion of a liquid to which we will direct the
attention of the student, is founded on a principle suggested by
the Hon. Mr. Boyle, for the determination of the relative density
of different fluids, and applied by MM. Dulong and Petit to the
investigation of the expansion of mercury. Although not so sen-
sitive in the appreciation of small changes of volume as other
methods which will be described subsequently, this method yet
possesses the great advantage of enabling the experimenter to
determine directly the true expansion of any liquid whose phy-
sical properties admit of its application, without a knowledge of
the expansion of the envelope in which it is contained.

The principle on which this method is based is, that if a
U-shaped tube contains in its vertical arms fluids of different
densities, when those fluids are in equilibrio, the weight of a
cylindrical column of the fluid in one arm, standing on any
base, is equal to the weight of a cylindrical column of the
fluid in the other arm, standing on an equal base in the same
horizontal plane; and the volumes of those columns will be
as their heights, since their bases arc equal. Hence we can

CHAP. I.] DILATATION OF LIQUIDS. 5!

•ly the ratio of the volumes of equal wci
me liquid at different temperatures, and consequently
ut dilierent densities, or, what is the same thing, the ratio of
the volumes of the same mass at two different temperatures,
from which we can calculate, as usual, the coefficient of ex-
ion for the corresponding change of temperature. For,
let the fluids in the two arms be at o° and <°, and conceive two
..drical columns standing on equal bases; let the heights
volumes of these columns be H0, Ht ; F0, Vt ; we have
: //,:#•<,; but Vt=V0(i +$<):- FoO+Sr): To :://,://..

. Ht-H0

and ct = — jj — .

•"o

The following is a brief description of the apparatus em-
ployed by MM. Dulong and Petit for the application of thisprin-
: a complete account of it is contained in their original me-
r, which appeared in the seventh volume of the Annales de

The tube containing the mercury, which, as we have men-
tioned, was the liquid to which this method was applied by
MM. Diiloni: and Petit, was placed, as in Fig. 23, on a strong
! liar of iron, furnished with two levels, and placed on a
<1 provided with levelling screws, so that the upper surface of
the i . and consequently the branch BC of the tube, could

perfectly horizontal. The branch BC and the lower
MIIS of the vertical arms were of very small diameter, for the
ninishing the mass of mercury employed in the
I also preventing the ivady communication of the
Is, at dili- .iperaturcs, in th<- BIB. Two pillars

i an indrx

1 of tin- bar was accurately determined, and,
6 temperature of o°, remained constant dur-
.vho leoC' . This pillar and the bar AH v.

,' d l»y a ; lei containiivj meltin

lion

in the tu!>e
i

ape-

DILATATION OF LIQUIDS. [BOOK I.

rat u re of 300° C. without boiling, and kept at a constant level
by means of a waste pipe. Plunged in the oil, parallel to the arm
DC, were two thermometers, one an air thermometer, constructed
in a manner which will be explained in the next section, the other
a mercurial weight tiiermometer. This latter instrument is similar in
its construction to that described in (30), and its application to
the measure of temperatures is easily explained. From what was
i in the passage referred to, it appears that if J-Fbe the weight
of mercury filling such an instrument at o°, w the weight ex-
pelled by the expansion due to the temperature t°, we have

jp ; but Ah the coefficient of relative expansion of mer-
cury in glass for £°, = Kt°, if -/The the coefficient for i°; hence

* = JC ~W * Similarly, if w be the weight expelled at T°, the

temperature of water boiling under a known pressure, we have

rr, I W ^ W W -W -

' = 17 TT ~ 5 hence t = 1 — - . -== , from which equation,

A // -w w W-w

knowing w in a given instrument, we know £°, the temperature
corresponding to jr.

The level of the mercury in the arm DC was always kept one-
half u millimetre (about one-fiftieth of an inch) above the level
of the surrounding oil ; this was effected by adding or removing

,iall quantity from the arm AB. A brick furnace surrounding
the copper cylinder was used for the purpose of heating the oil ;
and before making the experiment all the apertures of the fur-
nace were closed, by which means the oil could be maintained at
a constant temperature for a considerable period.

Such were the arrangements for determining the temperature

oi'the mercury in the two arms; it remains now to describe the

method of ascertaining the height at which it stood in them.

Tli is was effected by means of an instrument, since called a ka-

thetometer, and extensively used in physical investigations for

of measuring small diilerenees of vertical heights.

'I ins instrument (Kigs. 24, 25, 26) consists of a massive vertical

pillar a, standing on a tripod, which rests on levelling screws.

1 t<> the pillar, and move-able round it as an axis, is a

CHAP. I.] DILATATION OF I.U'IIDS. 53

finely graduated rule ll\ which carries a horizontal telescope d,

<>rt focus.* The telescope is also furnished with a spirit level

id a screw /•, for altering slightly its inclination to the ver-

atory to using this instrument, the pillar, or rather the

3 round which the rule and telescope turn, must be rein!

:ical, and the telescope itself truly horizontal; and
this will be known to be the case when the telescope pres<
nudity, as shown by its spirit level, during a com;
lution round the axis. The kathetometer being thus adjr.

^•ope is directed towards the index R, and the cross wires

in its locus brought to coincidence with the extremity of the

index ; it is then directed successively to the levels of the mercury

in AB and DC, and the quantities by which the telescope is de-

along the graduated rule measure the differences between

•altitude of the index and those of the mercurial columns;

and the height of the former above the base bar being known,

the heights of the latter are determined.

re was requisite, in the use of this apparatus, to insure

uniformity of temperature through the whole of the liquid in the

:.er cylinder; and the observations made with the kathetomc-

ired to be conducted with the utmost care, in order to

;n accuracy in the measurement of the expansions, as the

- of level in the two tubes was very small, b<
only i -f- 55. 5th part of the shortest between o° and 100°.

method MM. Dulong and Petit determined the co-
"f expansion of mercury, from o° to 100°, to be = i -H-
-. or the circulating decimal 0.018.

40. . />•/ method of ascertaining

a liquid from o° to *° consists in determining
•its »>f known volume of the liquid at o° and t°, from
Lculate th«- volumes of equal H OX of the

.-s of liquid at tho-e tw,, i

vcral ways.

id ma j be contained in an envel larto

bit capable of tMlngmorvd with fcnlk :m.i tii< .-.it.- a«ijiisii.

54 DILATATION OF LIQUIDS. [BOOK I.

in IMLT. 21, whose expansion has been previously determined

.msion of mereury by the method described in 30.

liquid, alter having been long ami carefully boiled, to free

it from air, is placed in melting ice, the orifice of the capillary

Mg kept immersed in a quantity of the same liquid, until

•.vhole mass has been brought to the temperature of o°. It is

then removed from the ice, and the temperature gradually raised

to £°, the liquid which escapes, in consequence of the expansion,

being collected in a little capsule. Let w be the weight of liquid

expelled, JIr-M' the weight of that remaining in the vessel at t°y

and let V0 be the volume of the vessel at o°, k its coefficient of

expansion for i°. Then we have from the experiment:

II ' the weight of the volume V0 of the liquid at o°, and

W- ic = the weight of the same volume V0 at t°t if we neglect the

expansion of the envelope.
U ' - ic = the weight of the volume V0 ( i + kt) at Z°, if we take the

expansion into account.

In the former case, as V0 is the volume of liquid at £°, corres-
ponding to a weight, W-w, the volume at the same temperature,

W

corresponding to the weight, Wt will be VQ — ; the apparent

expansion of the mass of liquid corresponding to the weight W
therefore from o° to t° is

v°W^~Vo =

and consequently the coefficient of apparent expansion

In the latter case the volume at z° corresponding to the weight
\V -ic, is Fp(n-fe); therefore the volume at the same tempc-

W

lature of the weight, W, will be V0(i + kt) -^ ; hence the real

expansion of the mass whose weight is Wis

W _ / Wkt +

CHAP. I.] DILATATION OF LIQUI 55

and consequently the coefficient of ;v«// exp:mM«m

• + w

-JT^-'

(2). The li<[iiid may be contained in a vessel similar to that
represented in 7, and the weight of the quantity filling it

up to a certain height. /////, at two temperatures, o° and d°, as
I. Then, the coefficient of expansion of the vessel 1>
known, the coeflieients ul' apparent and real expansion ol
liquid may be determined as in the last method.*

(3). Or lastly, a ball of some material whose expansion is
known, may be weighed in air and in the liquid, at the tempera-
tures o° and Z°, care being taken to allow the ball, on both oc
sions, to acquire the temperature of the liquid. Ifw be the dil-

:icc between the weights in air and in the liquid at o°, and
w at t°, we obtain, by a process of reasoning similar to that in
the preceding methods,

. which is called the areometric method, was employed by
M. ll;;l-tn"»m in the determination of the expansion of wai r; ii

.ipplicable. however, as well as some other <»f the preceding

im-thod.s to the case of such liquids as arc altered by oxygen or

moisture, as well as to those which arc highly vo-

41. 8, — The tltirJ method ofdcter-

the expansion of liquids consists in const meting with

Miilar to tin* ordinarv ones, and compa
•us with a standard mereiirial thennoin

M. I P 1 this method in an «'xt»-n

. whirli appear to h. eondnetctl witli

grCfi1 - and of which he ha> published a detailed account

in t' :h volumes ol'th,- A, males

,f </,' /'/I'^i./ne (3"'* Serie).

• Annalcs d< Giemie, 3"» Ser.,

56 DILATATION OF LIQUIDS. [BOOK I-

apparatus employed by M. I. Pierre consisted of a cylin-
drical vessel, AB, Fig. 32, of galvanized metal, twenty-five ccnti-
diametcr, and twenty-six centimetres high.

On its lid, AC, which was furnished with a tundish, E, was sol-
dered a rim. ///«', of the same metal, within which was fixed, by
means of a collar of leather, a cylindrical envelope of glass, twenty -

:i centimetres high and seventy-seven millimetres in diameter.
In the centre of the lid and of the rim was an opening with a
short flange, in which were fixed, by means of a cork, the stand-
ard thermometer, T, and the thermometer T', containing the liquid
to be examined.

The stems and reservoirs of these two thermometers were as
nearly as possible of the same dimensions, and the reservoirs were
always kept at the same height, so as to occupy the same stratum
of the liquid in the vessel AB, designed to raise their tempe-
rature.

Two other thermometers were completely plunged in the
water contained in the glass envelope, to the points to which the
liquids filling them respectively rose. The first, £, was a mercurial
thermometer, and had a very long reservoir, whose diameter dif-
fered little from that of the steins of the larger thermometer ; t'
was a thermometer containing the same liquid as T'. These two
thermometers were intended, the first, £, to give the temperature
of the water in the envelope, and of the portions of the stems
plunged in it, and t' to estimate the correction to be applied to
the apparent volume of the liquid in T'. ;

To maintain the temperature of the water in the upper vessel
constant, which was rendered difficult by its contact with the
lower vessel, AB, especially when the temperature of the latter
was at all elevated, a stream of water was conducted from a cis-
tern, R, through a lead pipe, into the lower part of the envelope,
and a syphon, SS'S", furnished with a cock, constantly drew away
an equal quantity from the upper part of the vessel. The quan-
tity of water necessary to be supplied from the cistern varied
with the temperature of AB, and was regulated by the cock, r.

A double agitator, ad'bb" cc'dd", served to agitate simul-
taneously the water in the two vessels, and to establish a uni-
lurm temperature in the liquid masses occupying them respcc-

CHAP. I.] DILATATION OF LIQUIDS. 57

ly. The upper part of this agitator is represented in plan
in Fig. 33.

temperatures above that of the surrounding medium, the
a placed over a large furnace, whose draught could
be so regulated as to maintain a constant temperature in the
apparatus, during each observation, for a period of fifteen or
;ty minutes. The agitator being kept constantly in motion,
the instant was noticed when the liquids in T and T' attained
r maximum heights, and those heights were observed by
us of a small horizontal telescope. The instant of the maxi-
mum of T' differed scarcely at all from that of T. The indi-
>ns of the thermometers t and t' were then successively
not*

When it was required to produce a temperature in AB 1
than that of the surrounding medium, a stream of cold water was
introduced through the tun-dish E, and an equal quantity drawn
i-y the cock B. When the temperature became stationary,
rock B was closed, the stream of cold water stopped, and the
itor kept in motion until the instant of the minimum in T
and T .

For temperatures below o° a somewhat simpler form of vessel

1, filled with a mixture of alcohol and water, and the

••t'n m of temperature was effected by surrounding the appa-

- with a mixture of pounded ice or snow and crystallized

. ide of calcium. By add in Lr suitable quantities of snow or

. a stationary temperature of- 35° C., or even - 36° C.,

was obtained for at least fifteen minutes, when the temperature

6 surrounding medium did not exceed + i° or + 2°.

. mometers employed in these experiments were con-
structed with every precaution, and the expansion of the ery.-tal
glass of which they were compose! ifloertained separately for
i ,:nd j.hvHeul properties of the liquid- •

.ined by M. I. I'ierre himself,
ilation of the observations was made as foil.

.Hire of the 1, ,-1 ;

I ed on the therm.'
upper vessel

5 8 DILATATION OF LIQUIDS. [BOOK I.

k' the coefficient of apparent dilatation of mercury in the glass
fonning the envelope of T : then the formula

X = x + nk'(X-0).
will give the value of X*
If now we denote

By V0 the volume at o° of the liquid contained in T' ;

By Vo the volume at o° of the part of the thermometer T' in

the lower vessel ;

By VQ the volume at o° of the part in the upper vessel ;
By Vf the total volume which the liquid would occupy at X° ;
By Sj. the coefficient of true expansion of the liquid for X° ;
By $t the same coefficient for 0° ; and finally,
By k the coefficient of cubic dilatation of the envelope of T' :

then we will have

r«-r.(i+8.).

VQ (i 4- kX) will represent the volume at X° of the liquid in the

lower vessel ; and
Vo ( i + kO) the volume at 0° of that in the upper.

And first it is requisite to determine what this latter volume
would become at X°.

Let U0 be the volume occupied by the liquid at o° in the ther-
mometer t' ;

U0' the volume apparently occupied by the same at 0° ; and
k" the coefficient of expansion of the envelope of t' :

then the volume really occupied by the liquid in t' at 9° is
U0' (i + k"B) ; therefore we have

' This equation is only approximately ft'

i ' * ould be strictly true if K repre- sul)8titute j^g (sO. ™ *hich cxpres-

sen ted the coefficient of dilatation referred s*on *' denotes the coefficient of apparent ex-

to the volume at 0; that is, if for A' we pansion referred to the volume at (T, as usual.

CHAP. I.] LAWS OF DILATATION OF LIQUIDS. 59

the volume at o° of the liquid which at 0° occupies F0"(i + kO),-
therefore the volume of this quantity at X° would be

RK.-(n-M)

u;(i+esr

consequently we have

and therefore

The volumes Vm V», F0", U0, U0' were all ascertained by gaug-
ing with mercury.

Laws of Dilatation of Liquids..

42. LAW I. — All liquids expand on increase and contract on di-
ntion of temperature.

A singular anomaly occurs in the case of water and some

saline solutions, which possess a point of maximum density, on

either side of which they expand, whether on rise or fall of

temperature. The following apparatus exhibits this property

in a very striking manner, ab (Fig. 28) represents a glass cy-

linder, surrounded at cd by a brass envelope. Above and below

envelope the cylinder is pierced, so as to allow the intro-

ion of two horizontal thermometers, e, /, fitted in pieces of

:. On filling the cylinder with water at the ordinary tempe-

rature, a little above the level of the upper thermometer, and in-

:rigorific mixture into the space Ix-twr.-n tlu- i-ylin-lcr

and envelope, after a short time the lower thermometer begins

11, and continues to do so until it has reached the ti-inj-

"t'ulmiit 4° Cent, above zero, at which |><>int it remains sta-

r this the upper thermometer, which had fallen slowly

to6°or7°C.. to fall JIIMIV rapidly, and continues 1'alling

I it reaches to o°, and tl surrounding its bulb is

60 L4WS OF DILATATION OF LIQUIDS. [BOOK I.

These phenomena may be thus explained. The water in the
space (••/, In-ill^ cooled by the effect of the freezing mixture, is
contracted in volume, and being thus rendered specifically heavier,
it lulls to the bottom of the vessel, while its place is supplied by
the lighter fluid from below, which, in its turn, is cooled, and,
being increased in density, again sinks down ; and this double
current of the colder and heavier water descending, and of the
warmer and lighter ascending, continues until the whole mass
below c has attained its maximum density. Meanwhile the
smaller mass of water above c has been slowly cooled by con-
tact with the glass cylinder, which, although imperfectly, con-
ducts the effect of the frigorific mixture, until it has attained
a density approaching nearly to the maximum. After this, the
reduction of temperature continuing in the portion cd, which has
attained its maximum density, this mass expands, and shortly
becoming specifically lighter than that above c, it rises into and
mixing with it rapidly reduces its temperature to the freezing
point. The stationary temperature, therefore, of about 4° C.,
which, as we have mentioned, is maintained by the lower ther-
mometer, corresponds to the maximum density of water ; and any
change of temperature, either above or below this point, pro-
duces a decrease of density, and consequently an expansion of
volume.

This property of water is attended with important conse-
quences in the economy of nature. It preserves the deep fresh-
water lakes and rivers in high latitudes from being completely
frozen, since, after having been cooled down to the temperature
of 4° by the effect of currents, as described above, they can only be
reduced below that by direct conduction, which, as we shall see
subsequently, is effected with the utmost difficulty through water
or ice.

In a scientific point of view, the determination of the tempe-
rature corresponding to the maximum density of water is a matter
of considerable interest and importance, as the unit of volume of
r, at its maximum of density, has been proposed as the unit
of weight to be generally adopted in scientific researches, and has
been actually adopted as such in France for all purposes.

The precise point of maximum density has accordingly been

CHAP. I.]

LAWS OF DILATATION OF LIQUIDS.

6l

investigated by several physicists ; its exact determination, how-
ever, is a problem of extreme difficulty, owing to the very slow
alteration which the density undergoes for several degrees on
either side of the temperature corresponding to the maximum,
subjoin a table of the results arrived at by several experi-
menters, and of the methods which they adopted.

TABULAR VIEW of the Results of the principal Experiments /

the View of determining the Temperature corresponding to

' ' / >'f

Name of Obsemr.

Method of Experiment.

Tempera-
ture.

Remarks.

Sir ( ,'den
and Mr. Gilpin*,
Lefevre Gineaub,

Honec

Second method of
densities.
Third method of
densities.
By means of appa-

3°.89oC.
4.400
1 6oc1

From direct obser-
vation.
Ditto.

The mean of two

Tralles . . .

ratus described
in p. 59.
Ditto.

j *u j \

42 ro

sets of observa-
tions, one made
bv coolinff water

Kumfordd, ....
II ill strom1', ....

Ditto.
Third method of

•OJU
4.440J

4 .I081

from the ordina-
ry temperature,
the other
heating it from

0°.

From calculation

Ditto'

Ditto.

4O3 I >

by means of the

formiil'i ri'i'iv-

Muncktr,

Method of gradu-

• .» f

* .780

8cntiii'r tin1 deii-

ated tubes.

J «/"s

riti<

ponding to tl i

[\ telllj

tures as Mi
taincd by c\
riii.

•Philosophical Transactions, 1792, p.

b Journal do Physique, tome xlix. (ann.

. 170.

lOMCtioUB, vol. V. (1805)

• hobon's .1 '805)

p. 228.

1 V weden, 1823.

Ann. <U- Clii 1825.

' Memoirs of Academy of Sweden, 1 833.
Annalcn di Poggendorf, 1835, I

f Memoirs of Royal Acadcn
I i. 1830.

62

LAWS OF DILATATION OF LIQUIDS.

[BOOK i.

Name of Observer.

Method of Experiment

Tempera-
ture,

Remarks.

Stamferh,

Third method of

3°-75Q

The mean of seve-

Ditto' . . .

densities.
Ditto.

3 .762

ral direct obser-
vations.
From calculation

IlulstromJ, ....
Dittok,

Ditto.
By means of appa-

3 -9°o
4 .004

by means of for-
mula.
From a combina-
tion of the results
Nos. 6, 7, 8, 9,

10.

Mean of two sets

Despretz1, ....

ratus in p. 59.

Method of gradu-
ated tubes.

By a method simi-

4.007
3 -982

of experiments
as in Nos. 3,4, 5.
From a graphic re-
presentation of
the curve of den-
sities, laid down
from direct ob-
servation.
From graphic re-

lar in principle
to that in p. 59.

presentation.

Sea water and water holding in solution various salts in diffe-
rent degrees of saturation, have also been found by M. Despretz
to possess a point of maximum condensation, in some instances
above, in others below that of ordinary congelation. We annex
the table of his results as given by M. Pouillet".

It may be remarked that M. I. Pierre has shown that a maxi-
mum density does not exist in any of the very extensive series of
liquids examined by him, except water or watery solutions.

h Annalen di Poggendorf, 1831, No. i.
« Ibid.

J Memoirs of Academy of Sweden, 1833.
Annalen di Poggendorf, 1835, No. 2.
k Anualen di Poggendorf, 1827, No. 4.

'Comptes Rendus, 1837, part i. An-
nales de Chim., &c., January, 1839.

m Ibid.

n Elements de Physique, 4me Edit., tome
i. p. 284.

CHAP. I.]

OF DILATATION OF LIQUIDS.

TABLE of the Temperatures corresponding to the maximum Density
of various aqueous Solutions.

Densities.

htof
Substantv in
997.45 of
Water.

Maximum.

Point of
Congelation.

Tempera-
ture during
Congelation.

Sea Water, .

1.027 a^2O°

*°67

'

- 2°.CC

- I .88

Chloride of

j J

Sodium, . .

1.009,, 6

12.346

4- I .19

I .21

0.71

:o, . . . .

I.OI8,, 6.26

24.692

I .69

- 2.24

I .41

to, ....

1.027 „ 6 .60

37.039

- 4-75

- 2.77

2 .12

Ditto ....

— 1 6 .00

— 4. .30

oride of

T j

Calcium, .

1.005

6.173

4- 3.24

- o .38

- 0 .22

Ditto, ....

I.OIO

12.346

4- 2 .05

- 0.53

- 0.53

Ditto, ....

1.020

24.692

4- O .06

- I .12

- I .03

Ditto, ....

1.031

37-039

2.43

3.92

- I .6l

Ditto, ....

1. 060

74.0/8

- I0 «43

- 5.28

- 3-56

Sulphate of

Potash, . .

I.OO5

6.173

+ 2 .92

- 0.15

- 0.15

Ditto, ....

I.OIO

12.346

4- I .91

- 0.27

- 0.27

Ditto

T O2O

2J_6O2

— o .10

- o .56

— o c6

to . .

*^.vry«

37.O39

- 2 .28

— 2 .OO

^ O

— o .77

Ditto, ....

1.058

74.078

- 8-37

• wy

- 4 .08

/ /
- I .50

;.hate of

la, ...
Mo

1. 006
I.OI2

6.173
12.346

+ 2 .52
4- I .15

- 0.27
i .14

- 0.17

- o-33

•:•>, ....

1.023

24.692

I .51

- 0.83

- o .69

Ditto, ....

1.034

37.039

- 4-33

' 2 .39

I .10

Ditto, .

1.066

74.078

- 12 .26

- 2.17

1 .13

Carbonate of

Potash, . .

1.033

37.039

3-95

3 .21

1 .17

Ditto, .

1.075

74.078

- 12 .41

2.25

- 2.25

Carbonate of

Soda, . .

1.039

37.039

- 7.01

- 2.85

'.37

Ditto

1.O7C

74.. 078

- 17 .30

- 2 .20

- 2 .02

Sulphate of

i j

/ T /

- o .62

I .32

- O .37

Pure Potash,

1.032

37.039

2 .10

j i
• 2.03

1.062

74.078

- '5 -95

4-33

Al<

0.988

j78

4- 2 .30

- 2.83

- 2.83

Sulphuric

I.O08

12.346

) .60

- o .47

- o .47

Dir

i .01 6

24.692

T /
I .09

T /

- o .90

1.024

? .02

LAWS OF DILATATION OF LIQUIDS.

[BOOK i.

43. LAW II. — Tlie amount of expansion of liquids is not pro-
portional, as in the case of solids, to their change of temperature ;
they do not, therefore, expand uniformly with mercury in glass, nor
indeed do any two liquids expand uniformly with one another.

The two following tables demonstrate this in a very striking
manner. The first, due to M. Deluc, was constructed as follows :
A number of thermometer tubes, with their stems accurately gra-
duated, were filled to a convenient height with the fluids enu-
merated, and then sealed with the precautions ordinarily used in
the construction of thermometers. The points at which the
liquid stood in each at the temperatures of melting ice and boil-
ing water were marked, and the intervening space divided into
eighty equal divisions, as in Reaumur's scale. The thermometers
were then all plunged into the same bath, whose temperature was
gradually raised by intervals of 5° R., and the number of divi-
sions occupied by the fluid in each, at the temperature given in
the first column, is registered in the succeeding columns.

TABLE of the comparative Indications of various Thermometers.

Mercury.

Olive
Oil.

Essential Oil
ofChamomile.

Essential Oil of
Thyme.

Water satura-
ted with MurL
ate of Soda.

Alcohol highly
rectified.

One Part of Al-
cohol and one
of Water.

One Part of Al-
cohol and three
of Water.

Water.

80

800

80.0

80.0

80.0

80.0

8o.O

80.0

8o.O

75

74.6

74-7

74-3

74.1

73-8

73-2

71.6

71.0

70

69.4

69.5

68.8

68.4

67.8

66.2

62.9

62.0

65

644

64-3

63.5

62.6

61.9

60.6

55-2

53-5

60

59-3

59-i

58.3

57-1

56.2

54.8

47-7

45.8

55

54.2

53-9

53-3

Ji-7

50.7

49.1

40.6

38.5

5o

49.2

48.8

48.3

46.6

45-3

43-6

344

32.0

45

44.0

43-6

43-4

41.2

40.2

384

28.4

26.1

40

39-2

38.6

38.4

36-3

35-1

33-3

23.0

20.5

35

34-2

33-6

33-5

3i-3

30-3

28.4

1 8.0

15.9

30

293

28.7

28.6

26.5

25.6

23-9

*3-5

II. 2

25

24-3

23.8

23.8

21.9

21. 0

19.4

94

7-3

20

19-3

18.9

19.0

17-3

I6.5

15-3

6.1

4-J

'5

14.4

14.1

14.2

12.8

12.2

u. i

34

1.6

10

9-5

9-3

9-4

8.4

7-9

7-1

i-5

0.2

5

4-7

4.6

4-7

4.2

3-9

3-4

O.I

-0.4

0

0.0

o.o

0.0

o.o

o.o

o.o

0.0

0.0

5

-4.1

-3-9

- 10

-8.0

-7-7

CHAP. I.]

OF DILATATION OF LIQUIDS.

The next table is due to M. Gay-Lussac ; it gives the amount
of contraction of four liquids, — water, alcohol, sulphuret of carbon,
and sulphuric ether, — for every 5° Cent., counted in each from the
point at which they boil in air. M. Gay-Lussac fixed upon this
as the point of comparison, because the integrant molecules of
all liquids appear to have the same cohesive power at their boiling
points; and he hoped to be able to obtain some general ex\

for the amount of their expansions in terms of their tempera-
starting from this point. In this he did not succeed, but
his investigations have led to one very striking result. On in-
specting the third and fourth columns of the following table, it
will be seen that alcohol and sulphuret of carbon contract equally ;
and M. Gay-Lussac has proved that equal volumes of these liquids
produce also equal volumes of vapours.

TABLE of the Contraction of the undermentioned Liquids for succes-
sive Intervals of 5°, counted from their Boiling Points, the Vo-
lumes at those Points being equal to 1000.*

Temperatures.

Wator.

Alcohol.

Sulphuret of
Carbon.

Ether.

0

0.00

0.00

o.oo

o.oo

5

3-34

5-55

6.14

8.15

10

6.6 1

11 -43

12.01

1 6. 1 7

15

10.50

17.51

17.98

24.16

20

'3'!5

24-34

23.80

5I-83

25

06

29.15

29.65

39- '4

3°

18.85

34-74

35.06

46.42

35

21.52

40.28

40.48

52.06

40

24.10

45.68

45-77

58.77

45

26.50

50.85

51.08

6j

5°

,56

56.02

56.28

72.01

55

30.60

.01

61.14

7*-3«

60

32-42

</>

66.21

34.02

70.74

70

35-47

75-4*

70

80. i i

"This n -MI It," says M. (iav-Lu-ar, "that aloilml and M»l-
!..,n dilat.- r.|ually, and pmdu uu<> volume-

I

66 LAWS OF DILATATION OF LIQUIDS. [BOOK I.

of vapours, is certainly very remarkable; it would seem to war-
rant the presumption that there is an intimate relation between
the dilatation of a liquid and the expansion which it undergoes
when reduced to the state of vapour. This ratio ought to be in-
dependent of the density and volatility of the liquids, or at 1
ought not to depend on these properties only, since in alcohol
and sulphuret of carbon they differ so widely."*

44. Formula representing absolute Dilatation of Liquids. —
As the expansion of a liquid by heat is not proportional to its
change of temperature, we cannot express its corresponding coef-
ficient by the simple formula,

i-fc,

as in the case of solid bodies (36). M. Biotf accordingly pro-
posed the following expression,

where a, I, c arc coefficients constant for all temperatures in the
case of the same liquid, but varying with different liquids. This
formula generally represents the expansion of a liquid with con-
siderable accuracy ; but M. I. PierreJ has shown that in some
cases we must adopt different coefficients in the upper and in the
lower parts of the thermometric scale. Thus in the case of amylic
alcohol, or fusel oil, the coefficients for temperatures from - 15° to
-f 80° C. differ from those suited to the range from 80° to 131°.
M. I. Pierre states also,§ that a formula of this kind fails to repre-
sent the expansion of water between the limits — 13°. 14 and 100°,
and that he has not succeeded in discovering any simple expression
which will do so.

If we consider the volume of a liquid at o° as equal to unity,

its increment for t° = &=«£+ bt^+ cfi, and its mean coefficient of

s>

dilatation at the temperature 2°, for i°, is expressed by — = a+bt

t

+ ct*. Its true coefficient, however, at the same temperature, is
expressed by the ratio of the increment of volume to the incre-

ment of temperature, that is, by -—3 — - = a + lit + ^ct2. In re-

" Ann. <!•• ("him. ct dc Thys., tome ii. J Annales de Cliimie ct do Physique,

p. 136. tome xix. p. 210 (3""' Scrie).

f TraitO <!>• PliyMijii-. tom- i. p. 210. § Ann. de Chim. et Pliys., xv. p. 351.

P. I.] LAWS OF DILATATION OF LIQUIDS. 67

to these coefficients, M. I. Pierre has arrived at the
following conclusions:*

(i). That in all the liquids examined by him the wan and
coefficients increase with the temperature.

(2). That the true coefficient always surpasses the mean at

peratures above o°, and that the converse holds true below
o°.

(3). That the difference between these two quantities is some-
times very considerable, amounting to 38 per cent, of the latter

}i°.8, in the case ofamylic alcohol, and to 27 percent, at 59°,
for terchloride of silicon.

(4). That the true coefficient increases sometimes with great
rapidity; thus, for an interval of less than 132°, its increment

.ds 80 per cent, of its original value, in the case ofamylic alco-
hol; and for a change of 59° it equals 53 per cent, in the case of

•iloridc of silicon.

45. ff'yv/y>/«V Representation of Curve of Dilatation of Li'

b, — These results admit of being represented graphically as
folio

: a line AD be drawn representing the apparent dilatation

ercury in glass from o° to 100°, and let it be divided into

100 parts, corresponding to the degrees of the mercurial thcrmo-

iiilercnt points, p. j> . /< , ^c., let ordinates be raised,

iiiLr, on the same scale as the base line, the absolute di-

ion of a liquid corresponding to the temperatures expressed by

• . Jy,. Ap\ Af", &c., and let the points A, o, o, o", i
be connected. The line passing through these points, if they be

M.'iitly numerous, will form a curve convex to the axis of the

issae, which in curve of dilatation, and w!

filiation i.- of tin- form

y = ax + bx1 + or3.

emitiea of the abscis- corresponding to

ires*, t + dt, we erect ordinal. '< , and ii

further connect the points J, </, and draw at (/ a tangent CM

•n, cuttiiiLr tin- axis of ;i'; .11 /,, tin'

lit of dilatation for i° at the temperature t will be

• Ann. dc Chim. ctde Pbys., tome xx. p. 351 (j~ Scric).

68 LAWS OF DILATATION OF LIQUIDS. [BOOK I.

represented by the ratio -r-, and the true coefficient by -7, Ab

and nb being expressed by the number of degrees to which they
correspond. And A a being produced to cut the ordinate db' in
c, and ad being drawn parallel to AB, the increment of absolute
dilatation at the temperature £, for the increase of temperature dt,
will be represented by cd, if calculated from the mean coefficient,
and by ad if calculated from the true, the change dt being sup-
posed, in the latter case, to be so small that the tangent am coin-
cides with the curve from a to a. We have seen above that ac,
in some cases, is equal to .38 cd. It appears also, from M. I.
Pierre's results, that the true increment of dilatation for the same
small change of temperature increases rapidly with the tempera-
ture : thus for amylic alcohol its value at 132° is to its value at o°
in the ratio of 180 : 100.

As in this construction the ordinates represent the dilatation of
the liquid under examination on the same scale as the base line
represents the apparent dilatation of mercury from o° to iooc,
it follows that the ratio of any ordinate to its abscissa expresses
the ratio of the dilatation of the liquid to the apparent dilata-
tion of mercury, for the change of temperature indicated by the
abscissa.

46. Relation between the Temperatures corresponding to abso-
lute and apparent Maxima of Density. — If a liquid admits of a
minimum dilatation, or, in other words, of a maximum density
above its point of congelation, the corresponding temperature is
given by the expression,

or a + 2bt + et2 = o

dt

while if we seek the temperature corresponding to the apparent
maximum in a given envelope, we will obtain it by differentiating
the expression for the apparent volume with respect to the tem-
perature, and equating it to zero.

This expression, as appears from (38), is,

i + A* = i + (a - k) t + bt2 + ct3,
where A< is the coefficient of apparent expansion, and k the co-

CHAP. I-

OF DILATATION OF LIQUIDS.

efficient of expansion of the envelope for i°. The temperature
corresponding to the apparent maximum, therefore, is given by
the expression,

, OT (a - *)

3e(* = o.

It we call (T) the temperature corresponding to the absolute
maximum of density, and Tthat corresponding to the apparent,
and neglect the term multiplied by c, which is, in general, ex-
small, we have, approximately,

consequently,

which exhibits the relation between the temperatures correspond-
ing to the absolute maximum and the apparent maximum in an
•.•nvelope of known expansion.

M. Biot* gives the following tabular comparison of the results
of this formula applied to pure water in various envelopes, with

ie experiments made by Mr. Dalton.f

Material of F.

Value of A for r R.

Temperature of apparent Maximum in
Degrees Kcnumur.

Calcu

0.000 030 03
o.oco 045 78
o.ooo 063 09

O.OOO 070 02

0.000072 66
o.ooo 10689

4°.236

5 -°7*
5.960

6-3'9
6.456
8.246

4.667
6 .000

222

'r>4

: "

Copper, ....
Bru^s. .

•r, . . . .

47. Abf . ^-r. — Tl.< coefficients

lutation of mercury from o° to 100°, 200°, and 300°, are
MM. I)iil«>nLr ;in«l Petit as follows :{

" Trait* do I1! . 140. holaon's Journal. \<1. x. p. 93, 1805.

i. p. i 24.

I AW- OF DILATATION OF LIQUIDS. [BOOK I.

| Temperatures deter -
Air Thermometer.

Mean absolute Dilatation of Mercury
for i°.

Temperature indi-
cated by tin-
Dilatation of Mercury
supposed uniform.

In vulgar Fractions.

In Decimals.

0*

too

2OO
300

O
I + 5550
I -5- 5425

i -j-5300

o.
o.ooo 1 80 1 80
o.ooo 184 331
o.ooo 1 88 679

o°.oo

100 .00

204 .61
3H-IS

In consequence of the uncertainty attached to these results,
owing to various causes, M. Regnault has repeated the experi-
ments on the dilatation of mercury, with a form of apparatus con-
structed on the same principle as that employed by MM. Dulong
and Petit, but considerably improved in its details. He has found*
that the expansion of mercury between the limits o° and 300° C.
i.- represented with remarkable fidelity by the formula

in which

Log b = 4.252 869 o,
Log c = 8.401 944 i,

T being the temperature as given by an air thermometer, and %T
the coefficient of expansion from o° to T°.

In the following Table, calculated by means of this formula,
the first column contains the temperatures ( T) ; the second, the
value of the coefficient §.,.; the third and fourth, the mean (S) and
real (A) coefficients of dilatation for i° C., calculated by means
of the formulae given in (44); the fifth, the temperature (6)
which would be indicated by a thermometer graduated on the
supposition of the uniform dilatation of mercury. These tempera-
tures are given by the formula

0=100 A;

0100

mid finally, in the sixth column are given the differences (6 - 7')
U-twcen the indications of such a thermometer and the standard
air thermometer.

* Memoires de 1'Institut, tome xxi. p. 326.

CHAP. I.] LAWS OF DILATATION OF LIQUIDS. 7!

TABLE of absolut>> Dilatation of Mercury from o° to 350° C.

Tem-
pera-
ture.

Dilatation of 1'nit
'mine fn.Mi
o' to T'.

ST.

Coefficient
of Dilatation for i
between o3 and T'.

£.

i>era-
Real Coefficient of ture deduced
Dilatation for i V from Dila-
betweeno'andr\ tation
I rcurv.
A. 0.

Diffea'iice
of
e and T.

9-T.

0

O.OOO OOO

0.000 000 00

o.ooo 1 79 05

o°

0°

10

o.oo i 792 o.ooo 179 25

o.ooo 1 79 50

9.872

- 0.128

20

0.003 590 o.ooo 17951

o.ooo 18001

19.776

- 0.224

3°

0.005 393 o.ooo 1 79 76

o.ooo 18051

29.709 - O.29I :

40

0.007201 0.00018002: 0.00018102

39.668 - 0.332

5°

0.009013 0.00018027

o.ooo 181 52

49.650 - 0.350

60

o.oio 831

o.ooo 18052

o.ooo 18203

59.665 0.335

70

0.012 655

o.ooo 1 80 78

o.ooo 182 53

69.713 -- 0.287

80

0.014482 j 0.00018102

o.ooo 183 04

79.777 - 0.223

0.016 315 o.ooo 181 28

o.ooo 183 54

89.875 - 0.125

100 0.018153 0.00018153

o.ooo 183 05

100.000 0.000

no 0.019996

o.ooo 181 78

o.ooo 18455

110.153 f ai53

12O O.O2I 844

o.ooo 18203

o.ooo 1 85 05

"0.333 h 0.333

130 0.023697 0.00018228

o.ooo 185 56

130.540 r 0.540

140 0.025555

o.ooo 182 54

o.ooo 1 86 06

140.776 -f 0.776

150 0.027419

o.ooo 182 79

o.ooo 18657

151.044 f 1.044

160 0.029 287

o.ooo 18304

o.ooo 18707

161.334 + 1.334

0.031 1 60

o.ooo 183 29

o.ooo 187 58

171.652

+ 1.652

1 80 0.033039

o.ooo 183 55

o.ooo i88oS

182.003

-f 2.003

190 0.034922

o.ooo 183 80

o.ooo 188 59

192.376

+ 2-376

200 0.0368II

o ooo 1 84 05

o.ooo 18909

202.782

+ 2.782,

210 0.038704

o.ooo 18430

o.ooo 1 89 59

213.210

, 210

2 2O 0.040 603

oooo 18456

o.ooo 190 i o

223.671

f 3.671

230 0.042 506

0.000 I 84 S i

o ooo 1 90 6 1

234-154

4-1)4

240 0.044415 0.00018506

o.ooo i y i ii

244.670

+ 4.670

250 0.046 329 o.ooo i B

o.ooo 191 6 1

255.214

+ 5-2'4

260 0.048247 o.ooo is

O.OOO 192 12

265.780

,-.780

0.050 171 oooo 185 82 o.ooo i

276.379

+ 6.379

280 0.052 loo o.ooo 18607 ' o.ooo 193 13

287.005

+ 7.005

290 0.054034 0.00018632 o.ooo i

r>59

+ 7

300 0.055 973

000018658 0.00019413

308.340

310 0.057917 0.00018683 0.00019464

.048

320 0.059*66 0.00018708 0.00019515

, .786

33O O.o6l82O O.OOOI8733 O.OOO!'

340.550

4- 10.550

340 0.063 778 o.ooo 187 58 o.ooo i

1 336

"

350 0.065743 0.00018784 o.oooi'

:.l6o

+ I 2. 1 60

\V. abj 1 of the values of the coelli- -i.MU> in ti

i Of «= I + at 4 b£* -i - »•/•', l'..r vmious li(jui.ls t-..]Mpil«-(|
M. I. Piem1 .m»l al-<> tables of tlie density and

M.M

II

^- - -r

-3

a

O rfoo r~- r^oo o

N r-~ r<«.3O O — •<}•
M o r^O O — to
vc 10 u-. r^ co r- Ooo TJ- <s ~ N oo r- N

tr;sc SC (S to r- r-OO SO O rfO 00 Tl- N
C fs ro O r^» T •••

O %
\s

•so" b «" o to to o' r-

OOOOOOo-OOOOOOOOOOOOOOOOOOOO

doooooooooooooooooooooodddop

OOW-tOTj-O-TQto

ocssso N N - torocoro

N O M f^.sO OO OO — •• OO
OO O fO O T to ^ •• OO **

r~-ONO CN tooo •<*•
OO NroQ^noo

r-so ~ Cv O so N

N oo o ro
oo wo r~- ^
rooo r-»oo

to t^o t^>a — ' O so "-so so tr> r-^so O N r^ co «- so — •J-OQ to ••J- •-< o « r-
co t^- ^.so ooo tooro-oo oo r^ oo oo -rj-oooco- r^o co-> r^-co

gOOOOOOOOOOOO^OOOOOOOOOOOOooo
oooooooooooooooooooooooooooo

doddddddddddd

ddddddddddd

O •»!• N t~- «^i «
O so «• r~ r» «
T!- O «O - «oo

»^r

i2

Tfoo «^)so so O W^N
roso ro r^oo O QSO
« w oo r^oo wso M

CNTJ-CVQ OOoo
sc Oso •^•r-~ O\oo
t^-o O

1-* OVNOO

CN O fOOO r---«so O Tj-tO^ N ^J- ly^.oo Tj-oo N O Cs Cv N M SO *^SO r
so - »or~N ^ o OO OCNTJ-IOCV- Qso r-QSO « r-ro CNSO oo O
^o O oc «^so N M vo w rj- r- r-~ ooo so(SNOooto«wo csso r- « oo

w O to o oc
rose to

to O toOO N M to OOO I—TON <S r)-NOO <SOOO O

ddddddddddddddddddddddddddddd

ocOO ro
tooo Cv ••
cocowo WO

^CN^O « Cv~r*>«-.v}CN Cs O
«m«- O sor^NONi-< SO O
SO Th U") \o ^O »^so SO SO SO «0 SO

00 0 OOOOOOO O 000 0 OOOOOO O 00

so •" w
^so fo «

, M q to « co

TJ- O O N 00

q c>

so* ^

»i- ON Tt- uo oo oso ro N to « M ^oo so CNtoNoo-OThNOON

r-Or^- O roNTj-T+-r»soCs ONOOCS>H oo Os«oo r^-cxo m ON « •*

tO'OO r>- «tOVO'tCN toso •-< SO C\SO TJ- TJ-r^OMNO N r^r^

ro - N M N r- r-so CNCOO QSON-H »s OSOSON«OOSOOOO

r-oo oo oo CS-^CNSO «CSONONOOOSO csNc* r~ tooo fS 1-1 M «s

OOO O d M M M M tf d 6 0 M M N « c4 M M « M « ro «

.

cc 2

" o-d^

'='='= • =: I

006' u Jd

t SB

•S ^ 5 ® I £ J 2 |T ' I rf rf * - ' '

v5=,^ < cr o: !•? j-1 •? 1 o 1 g I* I • 1 .§ I -J £ • a"

Wi I tliill! 1 lit f !!!!!! I :

•= --
O's

'- - '->

® .2 S?

= - £ -

l

*oso* r^-oo dsd>- N r

. , .

4 gllllll 1 41^

«
<

1 I

ds d - <^ M 4- to

MrttSr* <S (SH

o^

If

*5^?
-' 1C' 2

ro -

" - ^

z. ~

£ S

II

I

"vo£ O

To 2

i £ b

CHAP. I.]

LAWS OF DILATATION OF LIQUIDS.

73

TABLE of the Density and Volume of Water > from - 4° C., to i oo
C., according to M. Despretz. ( The Density and Volume at 4°
// us Units.)

Tempe-
rature.

Volume.

Density.

Tempe-
rature.

Volume.

Density.

~9

i.ooi 631 i

0.998371

46

I.OIO 20

0.989 903

-8

i.ooi 3734

0.998 628

47

i.oio 67

0.989 442

-7

i.ooi 1354

0.998 865

48

i.on 09

0.989032

-6

i.ooo 9184

0.999 °8z

49

i.ou 57

0.988 562

-5

i.ooo 698 7

0.999 302

50

I.OI2 05

0.988 093

-4

1.000561 9

0.999 437

51

I.OI248

0.987 674

-3

1.000422 2

o-999 577

52

1.012 97

0.987 196

- 2

i.ooo 307 7

0.999 692

53

1.013 45

0.986728

— I

i.ooo 2138

0.999 786

54

i-OI395

0.986 243

0

i.ooo 126 9

0.999 873

55

1.01445

0.985 756

I

1.000073 o

0-999 927

56

1.01495

o 985 270

2

1.000033 I

0 999 966

57

1.01547

0.984 766

3

1.000008 3

o-999 999

58

1.01597

0.984 281

4

I.OOO OOO 0

I .OOO OOO

59

1.016 47

0.983 798

5

I.O00008 2

0.999 999

60

i .016 98

0.983 303

6

1.000030 9

0.999 969

61

1.01752

0.982 782

7

1.000070 8

0.999 929

62

1.018 09

0.982 231

8

i.ooo 1216

0.999 878

63

1.01862

0.981 720

9

i.ooo 187 9

0.999 8l2

64

1.019 13

0.981 229

10

i.ooo 268 4

0.999731

65

1.019 67

0.980 709

1 1

i.ooo 359 8

0.999 640

66

1.020 25

0.980 152

12

1.0004724

0999527

67

1.020 85

0-979 576

'3

1.000586 2

0.999414

68

1.021 44

0.979010

14

i.ooo 714 6

o-999 285

69

1.022 00

0.978473

'5

1.000875 I

0.999125

70

1.022 55

0-977 947

16

i.ooi 021 5

0.998 979

71

1.023 15

0-977 373

i-

i.ooi 206 7

0.998 794

72

1.02375

0.976 800

18

i.ooi 39

0.998612

73

1.02440

0.976 181

'9

i.ooi 58

0.998 422

74

1.02499

0.975619

20

i.ooi 79

0.998 213

75

1.025 62

0.975 018

21

1.002 OO

0.998 004

76

1.026 31

0.974 3<54

22

1.002 22

0.997 784

77

1.026 94

0.973 766

23

1.00244

o-997 566

78

1.027 61

0.973 132

24

I.OO2 71

0.997 297

79

1.028 23

0-972545

1.00293

0.997 078

80

1.028 85

0.971 959

26

I.OO3 21

0.996 800

81

1.02954

0.971 307

27

1.00345

0.996 562

82

1.030 22

0.970 666

28

1.003 74

0.996 274

83

1.030 90

0.970027

29

1.00403

0.995 986

84

I.03I 56

0.969 405

30

I.Oc:

0.995 688

85

1.032 25

0.968 757

3'

1.00463

0.99 1

86

1.03293

0.968 120

32

1.00494

>5 084

87

I.0336I

0.967 482

33

1.005 25

1777

88

1.03430

0.966 837

'.00555

0.994 480

89

1.03500

0.966 183

I.OC:

o 994 104

90

1.03566

0.96;

I.OC'

> 799

9'

1.036 39

37

1 .00661

9*

1.037 10

0.964 227

38

i. 006 99

^058

93

1.037 81

0.963 558

39

1.007 34

0.9,, •

1.03851

-' 908

40

1.007 73

; 329

1.039

4'

1.008 12
1.00853

O-9<y i
0.991

96

97

1.039

1.04077

0.96 i
0.960 827

43

1.00894

0.99.

98

1.04 i

44

1.009 38

0.990 707

1.042 28

I.OC

100

1.04

0.95!

74

LAWS OF DILATATION OF LIQUIDS.

[BOOK i.

TABLE of the Density and Volume of Water from o° C. to 30° C.,
according to M. Hcilstrdm.

Tempera-
ture.

Density and Volume at o° taken as
Units.

Density and Volume at 4°.!, taken
as Units.

Density.

Volume.

Density.

Volume.

0°

.0

I.O

0.999 891 8

I. OOO 1O8 2

I

.000 046 6

0-9999536

0.999 938 2

i. ooo 06 1 7

2

.000 079 9

0.999 92° 2

0.999971 7

.000 028 I

3

.000 100 4

0.999 899 6

0.999 992 °

.000 007 8

4

.000 1 08 17

0.999 891 8

0-999 999 5

.OOO OOO 2

4.1

.000 1 08 24

0.999891 77

I.O

.0

5

.OOO 103 2

0.999 896 8

o-999 995 o

.000 005 o

6

.000 085 6

0.9999144

0.9999772

.OOO O2 2 6

7

.000 055 5

o-999 944 5

0.999 947 2

.000 052 7

8

.000012 9

o-999 987 2

o-999 904 4

.000 095 4

9

0-999 957 9

.000 042 i

o-999 849 7

.000 150 i

10

0.999 890 6

.000 109 4

o-999 782 5

.000 220 o

ii

0.999 8112

.000 1 88 8

0.999 7°3 °

.000 297 o

12

0.9997196

.000 280 4

0.999 6117

.000 388 8

'3

0.999 616 o

.000 384 i

0.999 5°8 o

.000 492 4

H

0.999 500 5

.000 499 7

o-999 392 2

.000 608 i

'5

0.999 373 i

.000 627 3

0-999 264 7

.000 735 7

16

°-999 234 °

.000 766 6

0.999 1260

.000 874 7

i?

0.999 083 2

.000 917 6

0.998 975 2

.001 025 9

18

0.998 920 7

.001 080 5

0.998 8125

.001 188 8

19

0.998 746 8

.001 254 8

0.998 638 7

.001 363 i

20

0.998 561 5

.001 440 6

0-998 453 4

.001 549 o

21

0.998 324 8

.001 637 9

0.998 257 o

.001 756 o

22

0.998 156 9

.001 846 5

0.998 048 9

.001 9549

23

0-997 937 9

.002 066 4

0.997 830 o

.002 174 6

24

0.997 707 7

.002 297 6

0.997 600 o

.002 405 8

25

0.997 466 6

.002 539 8

o-997 358 7

.002 648 3

26

0.997 2146

.002 293 2

0.997 107 o

.002 901 6

27

0.996 951 8

.003 057 5

0.996 843 9

.003 1 66 2

28

0.996 678 3

.003 332 8

0.996 570 4

.003 441 4

29

0.996 394 i

.003 6189

0.996 2864

.003 7274

30

0.996 099 3

.0039160

0.995 99 i 7

.004 024 5

47. Comparative Contraction of various Liquids, starting from
their respective boiling Points.— We will conclude this section by
stating the results of M. I. Pierre's investigations as to the com-
parative contractions of various liquids, starting from their res-
pective boiling points.

CHAP. I.] LAWS OF DILATATION OF LIQUIDS. 75

(i). In the first place* he has verified the law of M.Gay-Lussac
([>. 65), as to the equality existing between the amounts of con-

:ion, for the same changes of temperature, of equal volumes of
sulphuret of carbon and ethylic alcohol, taken at their boiling
poii

(2). He has shownf that amylic, ethylic, and methylic alcohol

w sensibly the same law of contraction, that is, that equal

volumes of those liquids, at their respective boiling points, will

their equality at all temperatures equidistant from those

(3). That the same law holds true for the bromides of ethyle
and mcthylc.

(4). And also for their iodides.

(5). That it is also true for the acetate of the oxide of ethyle,
and the acetate of the oxide of methyle.

(6). As also for the buty rates of those oxides.
From which he concludes, that "the agreement observed in
the progress of the contraction of the liquids contained in each of
those groups leads us to believe, that in general the homologous
compounds derived from ethylic and methylic alcohol, and pro-
bably those also from amylic alcohol, follow the same law of con-
ion, starting from the respective boiling points of those liquids,
ami comparing them at temperatures equidistant from those
point

( )n inquiring further, whether this law extended to all binary

1 in an analogous manner by the union of one com-

.'•nt, simple or compound, with isomorphous elements,

>le or compound, M. I. Pierre examined. lirst, some binary

groups formed by the combination of a common simple element,

and secondly, some formed by the combination of a coitij-mmf

nj.lc isomorphous bodies. Of the first class

groups, PhCl3, PhIJr3;t PhCl3, AsCk; Sn('l

ic, &c. (30* Serie), bromine are usually considered iaomorpliou.-.

tome xv. p. 401. as, altl...u,:l. , i,],irin.- ha< ,,,,t v, t lioen ob-

; 220. served in a cry.-t their corree-

• • • remarks 1 1 ind ponding combination* are of that character.

76 DILATATION OF GASES. [BOOK I.

SiCl3,* SiBr3; and of the second, C4H5C1, C4H5Br; C4H5C1,
1,1; C4H5Br, C4H3I; C2H3Br, C2H3I; C4H4C12, C4H4Br>.
The results of M. I. Pierre's investigations were :
(i). That in generalf two liquids formed by the combination
of a common principle with isomorphous elements follow diffe-
rent laws of contraction, starting from their respective boiling
points.

(2). That the difference of contraction increases, and always
in the same direction for each group, according as the distance of
the temperature of comparison from the boiling point increases.

(3). That this difference is sometimes very considerable. Thus
in the group consisting of the terchloride and terbromide of sili-
con, the difference of contractions of those liquids amounts to
one-half of the contraction of one of them.

DILATATION OF GASES.

48. Notice of early Experiments. — The earliest recorded ex-
periments on the dilatation of gases were made in the case of
atmospheric air by M. Amontons, and are described in the Me-
moiresde 1'Academie Royale des Sciences for the years 1699 an^
1702. He observed \ that the increase of the elastic force of air
produced by the heat of boiling water was equal to the third part
of the weight with which it was charged, if the experiment was
made in spring or autumn, when the atmosphere has a mean
temperature ; and hence he concluded, from Mariotte's law, that
the increase of volume of air due to a rise of temperature from
the mean atmospheric temperature to that of boiling water equalled
about one-third of its original volume, and this whatever its origi-
nal density might have been.

The subject of the dilatation of atmospheric air was subse-
quently investigated by M. Miguet,§ M. De la HireJ M. Stancari^f

* M. Pierre assigns for the bodies of this xx. p. 51.

group the formula SiCl, SiBr. This, how- J Memoires de 1'Academie Royale, An.

ever, is not in accordance with the gene- 1702, p. 4.
rally received view of their constitution. § Ib., An. 1708, p. n.

f Annales de Chimie (3™ Scrie), tome || Ibid. f Ibid.

CHAP. I.] DILATATION OF G.\ 77

of Bologna, M. Deluc,* Colonel Roy ,f and M. Saussure.j: Dr.
Priest jr§ !h>t extended the inquiry to otlier permanent gases, and
followed by MM. Monge, Bertliollet, and Vandermonde,||
M M. I )•• Morveau and Duvernois,f and M. Charley wlio, although
he did not publish the results of his experiments, had arrived
at the conclusion that oxygen, azote, hydrogen, carbonic acid,
and atmospheric air, all dilated equally between o° and 80° R.,
while for the gases soluble in water he found different values of
dilatation I'm- each different gas.

49. J/. Gay-Lussac s i — An interesting account

of the preceding methods is given by M. Gay-Lussac in the
introduction to his memoir on the dilatation of gases and va-
pours, in the forty-third volume of the Annales de Chimie.**
In this memoir M. Gay-Lussac has shown that the chief cause
of error affecting all those methods, and which led, in some

mces, to the most incongruous results, was the presence
of moisture in the apparatus made use of, which, furnishing

h quantities of vapour as the temperature increased, caused
the expansion of the gas to appear much greater than it
really was. Avoiding this source of error as far as possible,
M. ( iav-Lussae, by means of an apparatus described in the ine-
in«. ir above cited, arrived at the result that all gases and vapours
nded l»v equal quantities for equal increments of temperature ;
and that, for a change from o° to 100° C., this expansion aniou:

irt-, the volume at o° being represented by 100. As
M. < ac has not mentioned in his memoir havin«j n

correction for the expansion of the glass vessel in which the
gas was contained, it lias been suggestedff that the value of tin-
expansion, according to his experiments, was really 37.8 for 100

•< at o°, or 378 for 1000. M. Laplace, }J however, mentions
that M. Gay-Lussac, having repeated the experiments, at his

I.U., p. 36.

*f Annale* de Chimi. 764.

t Phil.-. Tran*., 1777, p. 704. i 37 (1802).

108.

;;o. H Laplace, M«

| Memotas de 1' Academic, An. 1786, p. 270 (1805).

•78 DILATATION OF GASES. [BOOK I.

request, with a different form of apparatus, on making all neces-
sary corrections, among which that for the expansion of the glass

<>lope is expressly included, arrived at the same value, 375,
for the expansion of all gases from o° to 100°, the volume at the
former being 1000.

The apparatus employed by M. Gay-Lussac in this latter series
of experiments, appears to have been that described by M. Biot
in his Traite de Physique,* and is represented in Figs. 30, 31.
A thermometer tube was carefully graduated into portions of
equal volume, and the volume of the ball at its extremity ascer-
tained in terms of the divisions of the tube. All moisture was
then expelled by filling it with mercury, which was boiled for a
considerable time. The extremity of the tube was then luted
into a tube of larger dimensions, containing the gas to be exa-
mined, and also a quantity of chloride of calcium or other desicca-
ting substance. The gas was admitted into the ball by introducing
a fine platina or iron wire into the tube, which, not being moist-
ened by the mercury, left a free space all round it, through which
the gas ascended and displaced the mercury, of which, finally,
there was only left in the tube a small quantity to serve as an
index. The tube, being thus filled with dry gas, was first placed
in melting ice, and the point marked at which the index of mer-
cury stood, and also the height of the barometer at the time
noted. It was next placed in the vessel represented in Fig. 31,
containing water whose temperature was gradually raised to the
boiling point, when the position of the index and the barometric
height were again observed. Let n express the number of units
of volume occupied by the gas at o°, and H the height of the
barometer, n its volume at the temperature T of boiling water,
and //' the pressure to which it was then subjected. The vo-
lume actually occupied at the temperature T7, and under the
pressure 77, was n(i + kT)9 k being the coefficient of cubical
expansion of glass for i°; and this volume at the pressure //

would have been ri(i + kT) -^ ; accordingly, the expansion of

TTi

the volume n was represented by n(i + kT) -jj--n, and the ex-

* Tomei. p. 182 (1816).

CHAP. I.] DILATATION OF GASES. 79

pansion of the unit of volume, or the coefficient, ar, of expan-
sion for T°, by

50. Dr.'Dalton's Ea-j . — A few months previous to
the publication of M. Gay-Lussac's first memoir, there appe.

in the filth volume of the Transactions of the Manchester Society,
published in 1802, a paper by Dr. John Dalton, which had been
read before the Society in the preceding year.

In this paper Dr. Dalton states as the result of his experi-
ments, that all gases and vapours expand equally for equal

iges of temperature, and that loco parts of any one of them,

J5° Fahr., become 1325 at 212° F. ; giving a change of vo-
lume of 325 parts for a difference of 157° F., and consequently of
372 for a difference of 180° F. or 100° C.

The accordance of this result with M. Gay-Lussac's is at first
y striking; it is not, however, in reality so close as it
appears to be, since the unit of volume is taken in the two cases
at different temperatures: at o° by M. Gay-Lussac, at 55° F. or
12°. 78 C. by Dr. Dalton. To obtain the coefficient of expansion
for 100°, referred to the volume at o°, from Dr. Dalton's data, we
may i • of the formula,

V i+gt

~r=7T^'

~e?, like solids, expand uniformly with the mercurial
I'litting in this rxpre^'mn lor T and t, 1000, and
1 2°. 78, and for V and t\ 1325 and 100°, wo find a for i° = .00392,
100° = .392, a result notably dillorent from M. Gay-
Lussac's.

51. i-y. — For upwards of thirty
rs the law of the equal dilatation of all gases was admi:

•cists of Europe to be tin- law of nature; and the
expansion assigned by M. ( . e, and con-

.13 was supposed, by Dr. Dalton's independent
was universally hold to be <•• If. I' x lish

t to point out that tie air

-lit lY«>iii that iriven by M ( i ••-. Li

80 DILATATION OF GASES. [BOOK I.

and that it probably did not exceed .365 of the volume at o°;
and since been confirmed, with numerical re-

sults slightly dilll'ivnt, by M. Pouillet, M. Magnus, and M. Reg-
nault. The two last-named experimenters have also shown that
the rate of expansion differs very considerably in different gases.
In these more recent investigations, as in the earlier, the me-
thods of experimenting have been of two different kinds: in the
first, as in M. Gay-Lussac's, the expansion is deduced from the
,;il increase of volume which a gas receives on change of
temperature, the pressure to which it is subjected remaining con-
stant ; in the second, as in M. Amonton's, the volume remaining
the same, or nearly so, the increase of its elastic force due to a
change of temperature is ascertained, and thence, by Mariotte's
law, its expansion under a constant pressure is calculated.

As instances of the application of those methods, we extract
the following description of two forms of the apparatus employed
by M. Regnault from his Memoirs on the Dilatation of Gases, con-
tained in the fourth and fifth volumes of the Annales dc Chimie
et de Physique.

52. Apparatus employed by M. IfognauU for determining di-
rectly the Dilatation of Air under cohsta^, Pressure. — The appara-
tus of the first kind, as employed by M. Regnault for determining
the dilatation of atmospheric air, was constructed and used as
follows :

A cylindrical reservoir, AB (Fig. 34), terminating in a ther-
mometer tube, was passed through the cover of a tin vessel, v,
containing some water. When this water was boiled, the va-
pour had to pass round the annular space, L, L', in order to escape
through the pipe M, thus preventing the temperature of the inner
wall surrounding the reservoir, AB, from being reduced below
that at which the water boiled under the existing atmospheric
ore, After a short time, when the temperature of the reser-
voir <1 to that of the vapour of the water, the extremity,
tli'1 tube was connected, by means of caoutchouc collars,
with the desiccating apparatus, GG. This consisted of two tubes,
i metre long and 2omm in diameter, filled with pumice
pounded and saturated with concentrated sulphuric acid. These
re connected with a small air-pump, p. When the re-

CHAP. I.] DILATATION OF GASES. 8 1

servoir, AB, was connected with this apparatus, the air was drawn
from it by means of the pump, and again slowly admitted through
the tubes, GG, by opening a cock communicating with the atmo-
sphere. This was done five-and-twenty or thirty times, until the
air in the reservoir and the tubes attached was perfectly dry.
The cocks communicating with the external air were then left
open, and the apparatus allowed to remain in this state for half
an hour or an hour. The desiccating apparatus was then re-
moved; this was done by first opening the joint, <J in order
that if, owing to any obstruction in the tubes, GG, the pressure in
AB was less than that of the external air, the pressure might be
equalized by the compression of the dry air between a and D into

reservoir. The joint, D, was then loosed, and the reservoir
left for some minutes in free communication with the atmosphere,
after which the end of the tube, CD, was sealed by means of a
blow-pipe, and the barometric pressure at the time noted. The
difference of pressures, if any, between the external air and the
steam in the vessel, v, as indicated by the manometer, FN, was
also observed. The reservoir, AB, was thus filled with dry air
under a pressure equal to the atmospheric, and at the temperature
T° of vapour generated under the pressure existing in the vessel,

The next step was to ascertain the contraction which this air
would undergo on being cooled down to o°, and the volumes
of the reservoir at o° and 7'°, or rather the ratio of those quan-

For this purpose the reservoir was removed from the chamber,
nd placed in the apparatus represented in p

35, its tube passing downwards through u hole in the circular
•rvoir itself, supported by three pieces pro-
• iii tin- plat'-, and fiirthi-r srcuiv.l 1 -iv\v,

' ' ihU upparut'. 1 an arm capaMe

• liir.Tcni civw, r. On

this i littli- p . whose lower pai;

littl- ">n, whi- 1 a -mail

foot, P, carri«'«l th«- arm, >/. through the end of \vhirh
passed a screw terminating above and below in .-lightly round. •«!
poiir h a man-

part of tin- tube, CD, was dir- ictly

82 DILATATION OF GASES. [BOOK I.

towards the foot, P', and the height was marked at which the
arm, m, should lc fixed, so that the little spoon, kt should be pre-
cisely at the height and in the direction of CD.

This being arranged, the apparatus was placed over a vessel of
mercury, in such a manner that the end of the tube was five or
« -nti metres below the level of the mercury. A fine file-scratch
had previously been made on the tube, CD, at the place where it
was intended to be broken. The point was then detached by
means of a forceps, and the mercury rose to a certain height in
the reservoir. This latter was next surrounded with snow or
pounded ice, and the apparatus was left in this state for an hour
or an hour and a half, until it was brought to the temperature of
o°. The little spoon was then advanced along the arm, m, until
the end of the tube was closed by the wax, and the height of the
barometer at the time noted. The arm, st, was moved along the
foot, P, until the lower end of the screw at its extremity reached
the level of the mercury; the ice was then removed, and the ele-
vated column of mercury allowed to assume the temperature of
the surrounding air.

It now remained to measure the height of this column, in
order to ascertain the pressure to which the air in AB had been
subjected at the temperature of o°. For this purpose the vessel
of mercury was removed, by previously taking away the support,
s, and the difference of levels of the upper surface of the mercurial
column, and the lower point of the screw on st, was measured by
a kathetometer, which read, by means of its vernier, the fiftieth
part of a millimetre.

The reservoir, AB, with the mercury contained in it, was then
removed and weighed. It was next filled completely with mer-
cury which had been well boiled to expel all air and moisture,
and finally surrounded with ice, its point remaining plunged in a
vessel full of mercury. At the expiration of an hour and a half or
two hours, when the mercury remained perfectly stationary at the
uriiice of the point, the ice was removed, and the mercury which
was expelled by its subsequent dilatation collected in a capsule.
The reservoir was then suspended in the vessel, v (Fig. 34), which
hud served to dilate the air ; the height of the barometer was
noted when the water contained in it boiled ; and the mercury,

CHAP. I.] DILATATION OF GA 83

which continued to be expelled from AB until it had acquired the
temperature of the vapour, still collected in the capsule. The

Ait of this quantity was then ascertained, and also the weight
of that remaining in the reservoir. All the data were then known
requisite to calculate, first, the expansion of the envelope ; se-
condly, that of the air contained in it.

For let

//• express the height of the barometer when the point of the

tube, CD, was sealed ;
7' the temperature at which the water then boiled in the vessel,

v;

// the barometric height when the point was closed with wax;
h the height of the mercurial column which rose into the reser-

voir ;

U' the weight of the "same column;
/T the weight of mercury filling the reservoir at o°;
ir the weight expelled by dilatation from o° to T\, the tempera-

ture of water boiling under the pressure II :
8 the coefficient of cubical dilatation of glass for i ° ; and finally,
coefficient of dilatation for dry air:

then to determine S we have, as in (30),

and therefore

Mi--*' ,'I + J

5550 M V 555°
Next to M «. If /' be the density of mercury at o°,

ii ir

— j- — is the volume of the air at o° and under the pre^mv
// //. whirh, :<• /A filled the

it ir // /, ir

D //

:"»scd to be i

84 1'II.ATATION OF GASES. [BOOK I.

and t

7- W' H

l

The mean of fourteen experiments made with this form of appa-
ratus gave a = 0.003 662 3.

53. Apparatus employed by M. Regnaultfor determining the Di-
latation of Air, from the Change of its elastic Force due to Change of
pcraturc. — In the second form of apparatus (Figs. 36, 37)
the air was contained in a ball, A, whose capacity equalled 800 or
1000 cubic centimetres. This ball was connected, by means of a
line thermometer tube, with the larger tubes, FH, u, represented
in profile in Fig. 36, and in full view in Fig. 37. These two
tubes were cemented into the iron socket, IH, by means of which
they had free communication, and which was provided with a
cock, K. The thermometer tube, dE, consisted of two pieces let
into the opposite arms of a small copper socket, mno, of three
arms, into the under one of which was cemented a short tube, op,
drawn out at its extremity into a capillary termination. The
temperature of the ball was varied by placing it in a vessel, MN,
which could either be filled with the vapour of boiling water, or
surrounded with melting ice.

In order to dry the ball, the tube, DE, was removed from the
copper socket, the extremity, D, of the latter closed with a cover
of caoutchouc, and the temperature of AB raised to that of boiling
water by means of the furnace under MN. The tube, op, was
then put in communication with the desiccating apparatus of
Fig. 34, and the ball, AB, dried in the manner described in the
preceding paragraph. In the same way the tubes, FH, u, were
also carefully dried, and immediately filled with warm mercury
up to the end, ED, which was closed with caoutchouc to prevent
the entrance of moisture from the atmosphere. The tube, DE,
was then introduced into the socket at D, which it fitted closely,
op still continuing in connexion with the desiccating apparatus.
Mercury was now allowed to flow out of the cock, K, until the
level in the tube, FH, sank to a fixed mark, a, and in consequence
«»f the connexion with the desiccating apparatus the space Da was
filled with dry air. Both tubes, also, FH and u, being in free

CHAP. I.] DILATATION OF GASES. 85

communication with the atmosphere, the mercury stood at the
same height in both. The tube, op, was now detached from the
drying apparatus, and its extremity, pt sealed with a blow-pipe,
the atmospheric pressure at the time being noted. The fur-
nace, o, which had heated the water in MN, was then removed,
and the air in A cooled, by first pouring cold water over it, and
finally surrounding it with melting ice. The elastic force of the
air being thus diminished, the mercury in FH had a tendency to

. but was kept constantly at the level a, by allowing a suita-
ble quantity of mercury to flow out through the cock, K. When
the ball, A, had attained the temperature of o°, the height of the
barometer, and the difference of level, ab, were observed, and
thus all the data were obtained requisite to determine the expan-
sion of dry air.

In making the calculations it is necessary to take into account
the small volume of air in the space, C?DEF, which remains through
the whole of the experiment at the temperature t of the surround-
ing medium. We will suppose the ratio of its volume, v, to that
of the ball, v, known by the method of gauging with mercury.

1 . : //be the height of the barometer when the tube, op, was

sealed ;

'/' the temperature of water boiling under that pressure ;
// the barometric height at the conclusion of the experiment;
li the dilference of levels, ab;

e volume of the space, £/DEF;
Fthe volume of the ball; and
F the temperature of the space C?DEF throughout the experiment,

8 and a having the same significations as before.

when the ball was surrounded with ice, the air under the
// //' oeeupied the Volume I' at the temperature o° 4
ne r at the temperature t°. At the temperature oc the

hcse volumes would have been F4 , and under the

i :

//,

when the ball was Mimmmle I

86 DILATATION OF GASES. [BOOK I.

vapour of boiling water, occupied, under the pressure //, a volume
\'(i c /') at the temperature T°, + a volume v at £°; therefore
at o°, and under the pressure //, this mass would have occupied
the volume

i + a T i -I- at

Equating these expressions for the volume of the same mass at o°
and the pressure //, and solving for i + aT, we get

I + a T =

*-K-V

The value of a determined by this method was a = 0.003

54. Modification of this Form of Apparatus, by Means of which
it may be applied to Hie direct Measurement of the Dilatation of
Air under constant Pressure. — A slight modification of this form
of apparatus fitted it for the direct measurement of the expansion
of dry air under a constant and given pressure. This arrange-
ment is represented in Figs. 38, 39. The tubes, FH, IB, were con-
tained in a rectangular vessel, two of whose opposite sides were
formed of plates of glass. This vessel was filled with water, which,
in order to insure uniformity of temperature through its different
strata, was frequently stirred by means of the agitator, ff'gg. The
tubes were fitted into an iron socket, which, instead of being fur-
nished with a single stopcock, was constructed as is represented
in section in Fig. 39. The cock, R, merely served to put the
tube, u, in communication with the exterior, but the cock, R',
served either to connect FH with u, as in (a), or simply to open
a communication between FH and the exterior, as in (b).

To use this apparatus, the ball, A, being connected as before
with FH, was surrounded with melting ice, the tube, op, being in
communication with the desiccating apparatus. Mercury was
now poured into the tube, BI, until it rose to the level, a, and
the cock, R', being in the position (a), the mercury necessarily
stood at the same height in both tubes. The tube, op, was then

••<!, the, barometric height noted, and also the temperature of
the water surrounding the tubes.

The ice having been removed, the water in the vessel, MN,

CHAP. I.] DILATATION OF GASES. 87

was brought to the boiling point. To keep the mercury in the
two tubes at nearly the same level, it was necessary to allow some
to flow out through the cock, R. A portion of air thus pa-
from the ball into the tube, FH, and the two columns standing
nearly at the same level, /3, their difference of height was mea-
sured exactly by means of a kathetometer, and at the same time.
the height of the barometer and temperature of the water round
the tubes noted.

To derive from this experiment the expansion of the air, it
was necessary to know the volume of the ball, A, the volume, r,
from E to a, occupied by the air in the tube, FH, when the bull
was surrounded by ice, and the volume v, from E to b, when
the ball was at the temperature of boiling water. The first vo-
lume was easily determined by filling the ball with mercury at
o°, in the manner formerly described. The volumes v, v were
determined as follows :

The point, _j >, was broken so as to put the interior of the tube,

EF, in communication with the atmosphere. Mercury was then

poured into BI until it rose to y. The cock, R', was put in the

position (£), and the quantity of mercury was collected and

lied, which flowed out while the level was falling to a; this

served to give the volume u; the quantity was then collected

which escaped on the level sinking further to /3, and this, added

•rmer, determined v. For let w, w be the weights of

mercury corresponding to the two volumes, t the temperature

of the water; then w (i + ), w (i + j, are tin

V 555°' V 5550/'
of mercury at o°, which would fill those spaces; and accordingly

w t \ , w ( t \
~7T ( l + )» v = Trl l +

D \ 5550; D \ 5S5o)

should he added th.-
tubes outside the vessel in whn.li the water was hoiled.
mil's apparatus this ded the

I -r- 2000th part ni'the velum-' of thfi hall.

relation j the data of t: iinent

it a,

88 DILATATION OF GASES. [BOOK I.

Let // be the barometric height when the ball was surrounded

witli melting ice;

// the small difference of level at the same time in FH and IB;
// the height where the ball was surrounded by the vapour of

boiling water;

h the difference at the same time of levels in the tubes ;
*° the temperature of the water surrounding FH and BI during the

first part of the experiment ;
(Q during the latter.

Now when the ball was at the temperature T° of boiling water,
the air, under the pressure H' + h\ occupied a volume V(i +$T),
at the temperature T° + a volume v at the temperature t' ; there-
fore at o°, and under the pressure H+h, it would have occupied
a volume

V N H' + ll

+ at'J H+h ;

but in the first part of the experiment the same mass of air, under
the pressure H+ h, occupied a volume Fat o° + a volume v at
t° ; therefore at o°, and under the pressure H + h, it would have
occupied the volume

V+- —

Equating these expressions for the volume of the same mass of air
at the same temperature and pressure, we obtain the result,

55. Application of preceding Methods to the Case of other per-
manent Gases. — We have hitherto supposed the apparatus em-
ployed in the determination of the expansion of air. If any of
the other permanent gases are operated on, after the balloon has
been perfectly dried in the manner already explained, it is ex-
hausted, and put in communication with the gasometer by means
of a second tube in the lower part of the pump p. The gas is
then admitted, and withdrawn through the desiccating apparatus,
four or five times, until we are sure of its perfect freedom from
moisture. The remainder of the operation is then conducted in
the same manner as in the case of atmospheric air.

(HAP. I.] LAWS OF DILATATION OF GASES. 89

It' we wish t<> operate on air under a constant pressure greater
or less than the atmospheric, it is only necessary to force it into

hall, or draw it from it, until its pressure reaches the desired
limit, as indicated by the height, A, of the mercurial column which

•lances in in, and throughout the experiment to maintain

•e, this height, //, as nearly constant as possible

r.t ,,f Dilatation of Gases.

/siir.'i <>f I)'<l<it,if't»n under tfo atmospheric 7V..«.v»//v.— In the
1 80 1 Mr. Dalton* announced as the result of his investiga-
. tliat all ela>tic fluids under the same pressure expand equally
bv heat, and that for any given expansion of mercury, the corres-
pond ing expansion of air is proportionally something less, the
tlir temperature.

t coincidence not unusual in the history of the physical

A ' ic arrived, about the same time, at similar

. .It lumgh his experiments were not published until a

few months alter Mr. Dalton's. M. Gay-Lussac states his results

as foil

( i ). " A .-. hatever be their density, and the quantity of

r which th<-y hold in solution, and all vapours, undergo the
same dilatation bv the same change of temperature*11

(2). "For the permanent gases, the augmentation of volume
•h of them receive^ I'roin o° to 100° is 100 -f- 266.66 o£-
uitial volume at o°." „

Ace' M . 1 > ilton, a gaa at an y temperature incn

in volume I'm- a cliange n[' temperature oi' i° by a cnn.-tant fraction
•'////•// /. // I '• it according t«» M. ( iav-Lu-

at any t- 1'or i° is a con>tant Iracti"!

. According to the 1;:

• llici-'iit of cxpaiiHon tor i , the unit of v».lume at
o° becomes, at t°, (i + a)'; according t«> t
I +at. The ', rally o.M>id«-n-d to he con

ion of gases are ;il\va\ I to

•luine at o°.

• rt ii. p. 600.
I

9o

LAWS 01- DILATATION OF GASKS.

[BOOK i.

uefl expand uniformly with the mercurial thermometer,

at lca>t 1'i'twivii o° and 100°, the formulae (36) applicable to so-
lids apply uU> to tin' m.

Those laws of Dalton's and Gay-Lussac's have, however, been
found, as we have seen, to be only approximations to the truth.
Gases have not all the same coefficient of dilatation, nor is this
coefficient constant for the same gas under different pressures.
They are, however, true, in M. Regnault's opinion,* at the limit,
that is, they approach more nearly to the truth according as we
apply them to gases in a greater state of dilatation, and are strictly
applicable to a perfect gaseous state.

\Vo subjoin a tabular view of the results of recent investiga-
tions on the expansion of gases under the ordinary atmospheric
pressure.

TABLE of the Coefficients of Expansion of Gases from o° to 1 00°,
under the Pressure of 760""".

(. According to
M. IJudberg.f

According to
M. Pouillet.J

According to
M. Regnault.§

According to
I\l. Magnus. ||

I

0.366 130
0.367 060
0.366 880
0.370 990
0.371 950
0.387 670
0.390 280

0.365 659
0.366 508

0.364570

0.368 ooo

Carbonic oxide, .
Carbonic acid. .
Protoxideof azote,

0.369 087

Sulphurous acid,

0.385 618

The valuesf given in the fourth coltmn were obtained by
M. EtegatnH by the direct method of dilatation (54).

II" remarks that the coefficients of carbonic acid gas and
protoxide of azote, obtained by this method, were greater than
those determined by the method of elastic forces. The difference

• Annalra de Chimie et de Physi'|ii<!
(3roeSerio), tome v. p. 83.

t Taylor's Scientific Memoirs, vol. ii. p.
5.6.

* I :ipmensde Physique (4m< Kdit.), tonic
i. p. 259.

unales de Chimie et de Physique,
tome v. p. 75.

|| Transactions of the Royal Academy of
Ucrlin, 1841, p. 80.

^[ It may be remarked, that adopting the
value .36666 for the cooflicient of the dila-
tation of air, tliis coefficient may be ex-
pressed by the equivalent vulgar fraction
1 1 ~- 30, which will be found very con-
venient in calculations.

CHAP. I.]

•1LATATION OF GASES.

between the results of these methods is still greater in the case of
the more compressible gases, as cyanogen and sulphurous acid.
Thus for sulphurous acid he obtained, by the first method, the
value 0.390280; by the latter, 0.384530; and for cyanogen, the
values, 0.387670, and 0.382900. The difference between t-
two methods shows that, in the case of highly compressible gases,

to be strictly applicable.

ij ,>f It'il.ilnt'njn Jim/el' l)r>'*.<nirc* <tr,«t- /• and It M thun the.
Arm''*fheric. — On comparing the expansion of gases at different
jnault found that the coefficient increases with
the pressure. The following Table exhibits his results in the c
of air. as derived from the method of elastic forces (53).

TABLE .-/«>"•; ,i;r ?/<>• A>//^///>/n// ,,f Air under different Pres**

Pressure at o\

ire at ioo\

Density of Air at o',
taking u 1'iiity the
D.'ii-ity «f Air at o'
uiuU-r the Pressure
of 76omm.

I -f ioo a.

".72

'74 -36
.06

374 -67
•23
760 .00

i4y"im.3i
237 .17
395 -07
510 -35
510 .97

0.1444

0.2294
0.3501
0.4930
°-4937

I.OOOO

1.36482

1.3<S587

1.36572

-S .40

y2 -53
2144 .

3^55 -5r>

2286 .09
2306 .23
2924 .04
4992 .09

2.2084
2.2270
2.8213

100

1.36760

1.36800
1.36894

.icnti conducted by the iaioe method l«ad to the i'ul-
in the case of carbonic arid gas.

'

Mwrnt

I'

ioo a.

.0<;
.07

I23C

.03

I.OOOO

COMPARABILITY OF THERMOMETERS.

[BOOK I.

On in\v.-ti«::itintLr the relation between the expansion of:
and their pressure, by the direct method of dilatation (54) M. 1!
iiault arrived ut the following results:

Gases.

Value of i + 100 a under
the Pressure of >j6omm.

Value of i 4 100 a under
the Pressure of 2530""".

Hydrogen.

1.36613
1.36706
1.37099

1.36616
1.36944

i-S*455

\r ° '

Air

And for sulphurous acid:

Gas.

Value of i + 100 a under
the Pressure of 76omm.

Value of i + 100 a under
the Pressure of 98 2mm.

Sulphurous acid, . . .

1.39028

1.39804

From these tables it appears that the difference between the
coefficients of expansion of gases increases with the pressure to
which they are subjected, and hence the conjecture which, as
we have stated above, M. Regnault has advanced, that Dalton and
Gay-Lussac's laws, as well as the law of volumes, &c., are true of
gases at the limit, that is, when they are taken in their greatest
state of dilatation.

The remarkable increase in the expansion of sulphurous acid
tor so small a change of pressure as that from *]6omm to 980™™
i' -nilei's it probable, as the same author has observed, that vapours
have coefficients of dilatation very different from that of air at
t"i.iperatures not far removed from their point of condensation.
The importance of this remark will be seen when we come to
treat of the density of vapours.

IV. — ON THE COMPARABILITY OF THERMOMETERS AND THE
MKASURE OF TEMPERATURES.

58. Mercurial Thermometers. — It has been shown (10) that
thermometers constructed of any material, for which the increment
<>!' volume for any given rlumire of temperature bears to the origi-

CHAP. I.] COMPARABILITY Ol- THKKMOMETERS. 93

nal volume a constant ratio, and which are graduated according to
the method there explained, are perfectly uniform and comparable
in their indications. It was there also assumed that mercury in
dtils the former condition; but careful experi-
ments have shown this assumption not to be strictly true, and
mercurial thermometers, when exposed to high temperati
irreat changes of temperature, especially if made of different
kinds of glass, not only fail in being perfectly comparable, but
that even the same thermometer is not strictly uniform in its in-
dications.

The following table, given by M. Regnault,* establishes the
termer assertion. The temperature was ascertained by the me-
thod of weights. The thermometer, No. i , was formed of a piece
of ordinary thermometer tube, with a ball blown at the end; No.
2, of a small globe of the same description of glass, united to a
capillary tube; and No. 3 of a ball blown on a tube of crys-
tal glass. The three balls had sensibly the same diameter, and
the tubes the same bore and length

' •

2.

3-

twa i.. tu.-rii
i 3.

0 0°

o

0°

100

100

100

0

190.51

190 .84

191 .66

+ 1 .15

24'.

247 .02

249 .36

+ 2 .68

25,

252 .06

254.57

+ 2 .70

t .08

279.31

282 .50

+ 3 -4^

310.69

1 333.72

JII-I4

333 -76

315.28
340 .07

+ 4-59

ofuniiormity in the indications of tin- .-ami- tin
1 from a ] \\ <• disphu-rmrnt <'!' tin- o\ has lu-m

it in addition to this SOUK' ivseaivhr- 1>\ M.
uiiilt and M I. l'i«-nv >li»\v that tin.- point, as wrll as tin-
• it and IOC , arc li;iM<- to mvgular rliai

'.in-iil of i ( '., in the

<;4 COMI'AKAIUI.ITY OF THKRMOMKTKRS. [BOOK I.

and t-» an alteration equivalent to o°.6 in the length of the
column between o° and 100°.

co. Air '/'/ti'.nnoim'tt'rs. — The differences in the indications
i.f mercurial thermometers formed of different kinds of glass arise,
doubtless, from the fact that different glasses have not only diil'e-
ivnt coefficients of expansion, but also vary in the law of their
dilatation at high temperatures; and as the amount of absolute
dilatation of mercury is small, this variation in the expansion of
the envelope produces irregularities of considerable magnitude in
the apparent dilatation of mercury. As the real expansion of
air is much greater, its apparent expansion in glass is not affected
to the same extent by these variations in the rate of expansion of
the latter ; and accordingly in an air thermometer the rate of ex-
pansion of the glass may be considered as sensibly uniform. When
corrected, therefore, for the expansion of its envelope, such an
instrument forms the most perfect thermometer with which we
are acquainted in the present state of science.

Any of the various forms of apparatus devised for the purpose
of ascertaining the expansion of air may be employed, when this
expansion is known, as an air thermometer. The volume occu-
pied by the air in the instrument at o° being known, its true in-
crement at any temperature, — derived from its apparent incre-
ment and the expansion of its envelope, and corrected for varia-
tions of pressure, — divided by its volume at o°, is the index of the
temperature; and this ratio, being divided by .00366, gives the
number of degrees expressing the temperature on the centigrade

60. Comparative Indications of Mercurial and Air Tliermome-
— The following table gives a view of the comparative in-
dications of an air thermometer corrected for the expansion of its
envelope, and of a mercurial thermometer constructed with the
p«Tuli;ir description of glass employed by M. Regnault in his ex-
periments. It will be seen the accord between the two instru-
ments is perfect up to 200° C.

CHAI'. I.

COMPARABILITY OK THKKMr

95

Air Thrnii.iiiifter.

Mrrvurial Tlu-riiium. t.-r.

DitVorence.

0°

0° 0

50

50.2

-f O .2

ICO

100 0

150

150 o

2OO

200 0

250

250.3

+ 0.3

300

301 .2

-1- I .2

325

326.9

-f I .9

350

353 -3

+ 3-3

"These results apply to the comparative progress of an air
thermometer, corrected for the expansion of the glass envelope,
and a mercurial thermometer constructed with glass tubes of
.eh manufacture, identical, in short, with those employed in
my experiments. The correction might be very different if the
mercurial thermometer were constructed with glass of a different
kind

61. Changes of Temperature as measured by Air Thermome-
ters, fort i-- voted proportional to the Quantities of ffeat pro-
ng tlio.<c Clnnges. — When Pultun and (Jav-Lussac's laws,
however, of the equal dilatahility of all gases, were first an-
nounced, pli\ .ere of opinion that the air thermometer
Dot only best fitted t<» >erve for the indication of temperatures, but
that it was also capable of measuring the forces to which cha:

inperaturc are due. F,,r. th«-y anjued, a< the power of heat

latalion of volume is the >ame in all gases, how<
may dill'er in their physical propi-rtirs. we must conclude
•-nly that the mutual attraction of the molecules ot'lj...!:
oved when they a-Mime the n ,1.-, hut also that the

specific action of those particles ^\\ lieat, which might modify the
!' the latter, cease to h: inllumce. That

ithoiit any deduction

::minution in the dilatation of gases, and that this effect,
iy be assumed as the : the power \\hich

it.f

Annnli-i A v. (3wr Scrio) p. 100.

' i.-e).

96 i OMPARABILITY OF THERMOMETERS. [BOOK I.

62. Determination, on t/ri$ Hypothesis, of the absolute Zero.—

1 1 nee they were led to form certain speculations relative to the
absolute zero, that is, the point on the thermometric scale at
which the amount of heat in a body would be reduced to nothing.
This point they investigated thus. As the expansion of a gas
is the measure of the force or quantity of heat producing it, \vo
may assume as the unit of heat the quantity producing an expan-
sion of the unit of volume ; now taking the expansion due to a
change of temperature of i° C. as the unit of volume, a mass of

gas at o° contains, according to Gay-Lussac, 266- units of volume,

and therefore 266- of heat. Subtracting, therefore, this number
of units of heat from it, which, as we have seen, would reduce its
temperature to - 266- C., the quantity of heat which it con-
tained would be totally exhausted, and therefore the absolute
zero corresponds to the temperature of - 266- C.

This determination of the absolute zero appeared to be con-
firmed by some speculations of MM. Clement and Desormes on
the subject of specific heats, to which we will subsequently refer.
For the present we may state that the coincidence between
the two results can only be attributed to accident, as they are
both based on hypotheses which have been since proved to be
unfounded. The investigations of MM. Rudberg and Regnault,
which show the inaccuracy of Dalton and Gay-Lussac's laws,
overthrow all these views with respect to the air thermometer,
and reduce it to the same class with instruments constructed of
other dilatable substances, from which it differs only in its supe-
rior sensibility, and in the degree in which it possesses other im-
portant thermometric properties. It is still, therefore, entitled to
hold its place as the standard instrument for the measure of tem-
peratures, but can no longer be regarded as a true measure of the
forces producing changes in the latter.

63. Concluding Remarks on the Measure of Temperatures. —
In fine, the subject of the measurement of temperature stands thus.
Any substance possessing the property formerly referred to (10),
serves perfectly, when properly graduated, to estimate and indi-

CHAP. I.] COMPARABILITY OF THKK.MOMK, 97

temperatures, and it' we as.-ume as i ure of cl.

temperature the rll'ect of these changes in producing dilatation in

•ted, then, consistently with this definition.
f temperature is two, three, or four times another, it' the
n of the thermometric substance due to the former is so
manv multiples of that due to the latter. On comparing different

iowevcr, we find that although all, except liqu
TV well in the relation between their expansions and
changes of t .re from o° to 100° C., yet at higher tem-

B a notable difference is perceivable, so that the ratio
ro chants of temperature, measured by the corresponding
ns of one substance, differs sensibly from the ratio of
the same quantities as estimated by the dilatations of another.
question then an • what substance we shall fix upon

ur standard ; is there any one possessing any property mark-
/ suitable for this purpose, or do all differ
•ly in the f/*v//-,v in which they possess various properties,
•h render them, under different circumstances, more or less
so that our standard must be, to a certain extent, arbi-
trarily chosen? If we were acquainted with any body, or i
odies, whose changes of volume were proportional to the
5 producing them, such bodies would have a decided pecu-
liarity marking them out as suitable lor thermometric pur]'-

•iiuch as changes of temperature indicated by these would
i-oportional to the forces or quantities of heat to which t
iges were due. Such bodies gases were supposed to In .

: from Dalton's and ( Jav-1 .
the livj- upon them fall to the

and accordingly gases are to the same

with .1 ..urchoii fa standaxl

• •rmined liy Other coM>iderati«>ns which

have S(M-n, l.-ad ustoa«lo|.(

liiv of its indica-

;U)Lfe. limited nnlv bv the nature of its enve-

I, all

I'urpose to any other with
i

o

98 AIM'! ; 01 TI1K LAWS OF DILATATION. [HOOK 1.

thermometer, as in all others, by changes in volume of the ther-
mometric substances; that both these changes are co-ordinate el-
• - of a common cause, but that of the relation of eacli to
such cause we are yet ignorant; and that accordingly we are still
unprovided with an instrument whose indications of changes of
ti-Miperature are proportional to the forces by which such chai
are produced.

SECT, y. — APPLICATIONS OF THE LAWS OF DILATATION.

64. Measures of Length and Weight. — We have seen that the
absolute dimensions of all bodies are altered by changes of tem-
perature, and accordingly if these dimensions are expressed by
the number of the corresponding units, supposed to be of inva-
riable magnitude, which they contain, the value of the dimension
in question, whether length, surface, or volume, will vary with
the temperature of the body. If, however, we are acquainted
with its rate of expansion, and know the value of any of its di-
mensions at a given temperature, in terms of the invariable unit,
we can easily determine its value at all other temperatures. In
practice, however, it is impossible to determine any of the di-
mensions of a body in reference to such unit directly, as it can
only be ascertained by the application of a measure or rule which
is itself liable to contraction and expansion, and which, at some
given temperature, bears a known ratio to the corresponding unit.
In order, therefore, to ascertain the value of the dimensions of a
body, corresponding to various temperatures, in terms of the in-
variable unit, it is necessary to apply to the results of actual ob-
servation various corrections and reductions, which it is our pur-
pose to point out in the present section.

In like manner, although the absolute weight of the same mass
of matter, that is, its weight in vacuo, is not altered by changes of
temperature, yet its weight in air or any other fluid, and the ab-
solute weight of a given volume of it, as well as the ratio which

\veight of such volume bears to the weight of the same vo-
lume of any other substance selected as a standard of reference,
are all affected by such changes.

Before proceeding to point out the relations existing between

1 I ] APPLl* OF THE LAWS OF DILATATION. 99

the absolute- ami relative dimensions and weights oi . ami

iperature, it will not be irrelevant to our present sul
-..me remarks on the units to which these quantities are
lly referred.

Amongst

•ions we liiul that the ear! idards of length were

taken I'roin the human body; of this the £aicrvXoc* irot/c, cnnOaiu/.
-i)\rr. ami opyum of the Greeks, the ///*/////.<?. /»/*//»./•. yW/.

, passus, and »////« of the Latins, and the foot,
I, and fathom of the English, are obvious instances. IV

Miently iind a further ultimate unit, of dimen-
>o small as to be considered to require no farther subdivision,
and of u nature so constant rve to correct the great diver-

res derived from the sources formerly referred to. Of
this nature was the length or breadth of a grain of barley-corn,
which we find adopted as the ultimate unit by the Hindoos,
Hebrews, and several nations of modern Europe. Thus, in Eng-
land three barlev-corns taken from the middle of the ear, and
d end to end, formed the standard of an inch, twelve inches
•ituted a foot, and three led a yard, which was made the
unit for all higher denominations.

:ind, in like manner, the unit of weight freqiientlv de-
.nie source. "Thus, among th«- Hindoos, the
mined bv » to tin-

'/.v. whieh is considered equivalent
to two of tli.- li.rm.T. T • made t\v.. mr

• jiiivalent to the yiAk-or;. tlirir nu»t minute [
i money, four of these equal to the KC/EMITCO v, <>r eai-ob -

ih«« Oepnoc, or luj»inc. 'l'li<1 K»mans made their

:uinate in th«- • icriviiiLT

. irom the ' :uid theivt'^ie not wer

the Itali
and all otln-r ! n nations, the -rain ••!' 1-arlev mid tlie ,

the

S

: the pi.

'

I00 API NS OF THE LAWS OF DILATATION. [BOOK I.

. that one common measure and one common weight
vhoi. all through the kingdom. The weight which, in

accordance with this provision, it was the constant object of the

-lutuiv to establish, was that which has long been dcnomi-

1 the pound troy, and which contains twelve ounces, each
ounce being equivalent to twenty pennyweights, and each penny-
_ht to twenty-four grains. Besides this pound, howeverf
there has also been in use, from a very early period, another one-
llmrth irreater, culled the libra mercatoria, and nearly equivalent
to our pound avoirdupois of sixteen ounces, which was employed
almost universally in mercantile transactions, the use of the legal
and statutable pound, or pound troy, becoming gradually limited
to the precious metals, and, with a different subdivision, to medi-
cal purposes.

withstanding the various and repeated efforts of the Legis-
lature to secure uniformity of weights and measures throughout
the kingdom, it appears that, owing either to the inconsistency
of their regulations, the frequency of their changes, or the im-
perfections of the standards (made by rude artists, and tried by
methods equally rude), the desired uniformity was never attained,
and it was accordingly found necessary to appoint a Parliamen-
tary Committee in 1758, to inquire into the original standards of
weights and measures, and to examine those preserved in the

liequer, Guildhall, and elsewhere. The committee presented
their Report, which was drawn up by Lord Carysfort, on the
28th of May of the same year, and recommended that, in conse-
quence of the diversities and inaccuracies of the old standards, a

vanl and pound troy should be made by Mr. Bird, from the

mean of those preserved in the Exchequer, or rather from accu-

.. hich had been made of them, by Mr. Graham,* for

* It appears from tin: paper in the Phi- chequer, and representing a vanl, very

1 ^'.phical Transactions (.vol. xlii. p. 541), coarsely made, anil ruddy divided into

\\hich .--count of Mr. (iriihum's three feet, and one of the feet into twelve

eoniparisoij of the old ,-tandards with one inches, stamped uith an old Kn^lish 1)

which had l.cen mad<- for the, Koyal So- and a crown, and supposed to have heen

indned thott contained in the standard lodged there in the rei^n of

tin- K\che<|iicr, tin- (iuildhall, the Tower, Henry VII. In the same oll'u <• v, « -i
and in the,, nice of the riorkina!.. K Timi other squared rods of I trass, used as (In-
i lie in...-! ancient wa> an standard yard and ell, about half an inch in

i in th« l-;.\- breadth and thickness, and fitted into hollow

I.] APPLICATIONS 01- THK LAWS OF DILATA ! IOI

. and that these >hould be adopted as the stan-

the kingdom. A ; Report was made in tlie fol-

but the bills founded upon them, and proposed in

• •d the sanction of Parliament.
67. / — Shortly 1

Union, the subject of establishing a uniformity of weights

rencc to an invariable standard determined

tie principles, engaged the attention of the French Go-

.d on the motion of M. Talleyrand in 1790, the (
stiti: mbly appointed a commission consisting of MM.

.inge, Laplace, Monge, and Condorcet, to report on
ures proper to be taken to effect this object. Their II. •-
. delivered in the following year, after noticing the propo-
whieh had been made to adopt as the unit of measure the
: a pendulum vibrating seconds at the equator, or at
:iieir objection to the adoption of such standard,
.Yoking the hrtrrogrneuus element uf time, recommended
that the loooooooth part of a quadranta! arc of a meridian on
nidi's surface should be adopted as the primary standard of
. :h. weight, and capacity, under the denomination of a ;//•
nine tliis length an arc of the meridian, exten<
1 '..-mid be measured ; and that -

;bed, of distilled water at

of 0° C., should l»f determined as the unit of
ht, under the d<-H<_mation of a /V/M, munut, : and,
r, that the subd'n .oiild prociM-d ae-

de.

beds or matrices, cut on two sides of a sul-

-* bar, about from uliirii :

-•• were StampCll With ;i rn- \vnr<| <l.i>' C.iinpaiiy an. I tin- Mint w.-n- <i.

ii- lir-t jir<i|-i-:t! ! n^th

i of Queen EUzaVth ll \\a-> of tin- ]i>-n<liilnui a-, a >l.im!inl .

ho standard . laMi-h ill,- th. -how-

office* ae«m to have b»-< i

.

,Aii/,//'.s

1

102 APPLICATION- OF T1IK LAWS OF DILATATION. [BOOK I.

Tlu1 recommendations of this committee having been carried
into eileet, with this exception, that the decimetre cubed of dis-
tilled water at its greatest </<•;/*•////, and not at the temperature of
0°, :i ;>roposed, was adopted as the standard of weight,

•• the original metre* and kilogramme (les etalons prototypes) were
1 on the 4th Messidor, 1798, with a pompous address,
to the two councils of the legislative body. In speaking of the
metre it is said: ' Cette unite, tiree de plus grand, et des plus in-
variables des corps que le I'homme puisse mesurer, a Vavantage de
ne pas differer considerablement de la demitoise et des plusieurs
autres mesures usitees dans les differens pays: elle ne choque point
1'opinion commune. Elle ofTre un aspect qui n'est pas sans inte-
II y a quelque plaisir pour un pere de famille a pouvoir se
dire : Le chump qui fait subsister mes enfans est une telle portion
du globe. Je suis dans cette proportion conproprietaire du
monde.' " To provide against the loss of the unit resulting from the
possible destruction of the standard by " un tremblement de terre,"
or " un affreux coup de foudre," it is added that M. Borda had
determined with great accuracy the length of the second's pendu-
lum at Paris, and the repetition of the experiments at any future
period would furnish the means of recovering the original relation
of its length to that of the metre, and, consequently, of determin-
ing the length of the metre itself.

Notwithstanding all the facilitities, however, which the cir-
euinstanccs of France offered for the introduction into actual life
of a system of weights and measures founded on scientific princi-
ples, the opposition to its adoption, from prejudice or habit, was
so great, that in 1812 the Legislature was obliged to sanction a
partial return to the old system, and to this day the duodecimal
subdivision, and several of the names of the old measures, are ap-
plied to the new.

68. Determination of Standards in England ; Committee of
1818. — In the year 1818 the attention of Parliament was again
directed in England to the subject of uniformity of weights and
measures; and a commission was appointed, consisting of Sir Jo-

i Hanks. I*. II. S , Sir George Clerk. Mr. Davies Gilbert,

Knr\ r].p, cilia Metropolitana, Art. Arithmetic.

.P. I.] APPLI' ->F TIIK LAWS OF DILATATION. 103

\V. II. \V . Dr. Tli Unas Y -img, and Captain Kater.

!•• purpose of forming new standards of weights and n

or of determining the relations of those already in use to some in-

-Tandard exiting in nature. These commissioners pre-

•d three Reports, bearing date, re.-p.vtivcly, the 241)1 June.

1819, I3th July. 1820, and 3131 March, 1821. In the first of

;»orts they give it as their opinion, that with respect to

rtual magnitude of the standards of length there is no sufli-

t reason for altering those which at present are generally <-m-

and that there is no practical advantage in havl:
quantity cum mensurable to any original quantity existing, or
which may be imagined to exist, in nature, except as affording
little encouragement to its common adoption by neighbour-
ing nations. The great inconvenience, however, resulting from
a ch:mir«.' which would be so extensively felt, they considered to
outweigh the possible advantage which might accrue from its
adoption, and which would only affect those engaged in foreign
:al affairs and scientific pursuits. They recommended,

• over, the continuance of the existing subdivisions, both of mea-

- of length and weight, as being practically more convenient
than the decimal scale, inasmuch as they admit of a greater num-

••f divisions without the occurrence of fractional parts. Aj

unit of length they further recommended the adoption of

8 standard yard, employed for the measurement of

base on Hounslow Heath; but they subsequently, in their

nd Report, recommended, in preference, Mr. IJird'.- parlia-

-landard. < \reuted ill 1760. They further determined

th of a jH-ndulum vibrating seconds, in the latitude

11, at th<- I'-vel of the sea, and /// DOOI I to

; inches measured «>n thi- .-taudard ; and that the le:

j.latina metre at 32° F. e<jualle<l 39.37079 inches, the \

ird in l>"th C8 r at th<- trmp.-ratinv ol 6l I1'.

-|>CCt to n «>f \v«-ii/ht, li Mincnded that

;il»lc pound troy, made 1>\ Mr. Uird, should !>.•

•d as tlf -tandard pound tn.y; that this pound

760 grains, and that 7000 siu n should

delrnililir.l. f.l

purj

104 AIM'I.ICATIONS OF THE LAWS OF DILATATION. [BOOK I.

ibie inch of distilled water in cacno at 62°, as opposed to

ghta also /// KUlfO, weighed 252.722 grains, and in air at lire

c temperature, and under the mean barometric pressure.,
252.456 grains.

As the unit of capacity they recommended the adoption of
the gallon containing ten pounds avoirdupois of distilled water,
at the temperature of 62° F., and weighed in air when the baro-
meter is at 30° ; and they determined the volume of this quantity
of water to be 277.276 cubic inches.

A Bill embodying these recommendations was drawn up by
Sir George Clerk, and passed in 1824.

The standard of length, then, in England, is Mr. Bird's stan-
dard brass yard at 62° F., and in France Borda's platina metre
at o° C. ; and in case these measures should be lost or destroyed,
the means of restoring them is provided by the known relation
existing between them and the length of pendulums vibrating
seconds in the capitals of the respective countries.

In the same way, the standard weight in England is Mr. Bird's
double pound troy, and in France M. Borda's platina kilogramme ;
and the means of reproducing those standards is derivable from
the knowledge of the volume of distilled water at a known tem-
perature whose weight is equivalent to them respectively.

We now proceed to point out the relations between the abso-
lute and relative measures and weights of bodies and their tempe-
rature ; and first of their weights.

69. Relation between absolute Weight and Weight in Air. — The
absolute wreight of a body, or its weight in vacua, is, as we have
remarked, independent of its temperature ; this, however, is not
the case with its weight in air. For from the principles of hy-
drostatics it appears that the weight of a body in air is less than
its weight in vacua, by the weight of a volume of air, at the exist-
ing temperature and pressure, equal to the volume of the body.
To obtain the relation between those quantities, let us suppose
that the body whose weight is sought, and its counterpoise, are
both at the temperature of the surrounding air, which we will
also suppose free from moisture. We will further suppose them
placed in perfectly similar scales. Then let W be the weight of
the body in vacua, v its volume at o°, k its coefficient of expansion

(HAP. I.] APPLICATIONS OF LAWS OF DILATATION. 105

for i°, and therefore r(i + kt), its volume at <°, the temperature
:ing at the time of the experiment; further let m be the
_ht of the unit of volume of dry air at o°, and under the ba-
rometric pressure //, its weight at t° and /<, the temperature and

-are during the experiment will be m -jj ; and accord-
ingly the weight of a volume v (i -f kt), under the same circum-
will be

h i + kt

' 77 ' i + at '

and consequently the weight w of the body in air will be

h i + kt

w =

// i +at'

In the same way, if W be the absolute weight of the counter-
poise, t?' its volume, and k' its coefficient of expansion, its weight w'
in air will be

TI7, , h i + kt
w = W - mv -jj - - ;

// i + at

but these two quantities arc equal to one another, therefore we

<_rht of a constant volume of any body also varies with

.s it is inversely proportional to the volume ocru-

1 by a constant weight at that temperature. Consequently,

if U". IT n -present tin- wrights of a given volume, at the tnnpe-

ratniv- /. / , of a body whose coefficient of expansion is /•, we

If i+fe'

W

70. Relation between tabu /' —In

the ratio whirh tin- weight of a given vdumc of any

body bears t<> tin- \v«-5ght d'tlic -amc volume ofsmur BabstelMM

i as a standard, varies with tl>«- t«-mj ii. Tim

• »r tal'ular d'-n-ity .•!' the l>ody,
I

100 APPLICATIONS OF THE LAW9 OF DILATATION. [BOOK I.

as referred to that standard, and we will proceed to exhibit the
relation which exists between it and the temperature of the body
itself, and of the standard to which it is referred.

For this purpose let W be the absolute weight of the body,

W

and V its volume at the temperature t°, then -^- will represent the

weight of the unit of volume at the temperature £°. Let Q, re-
present the weight of the unit of volume of the standard at any
temperature T\ then the density of the body corresponding to
the temperature t of itself, and T of the standard, and which
we will represent by />, is given by the expression,

To ascertain the density ZX, corresponding to any other tempera-
tures t' and T of the body and the standard, it is to be observed
that the volume of the body, which at t° was equal to V, at t° is
equal to

v i + Sr

778T'

if Sh 8t; express the coefficients of expansion from o° to t and t'
respectively ; and similarly the weight of the unit of the standard,
which at T was Q, at T' becomes

I + A.

Ar, Ar/ expressing the coefficients of its expansion from o° to T
and T'. Therefore we have

F i + &, Q,' 1 + A/
or

i +S/ i+A/

In the case o£ gases, the weight of matter contained in a given
volume depends not only on the temperature but also on the
pressure. Hence the pressures, both of the gas whose density is
sought, and of that to which it is referred as a standard, must be
taken into account.

CHAP. I.] APPLICATIONS OF THE LAWS OF DILATATION. 107

Let D be the density of the gas at the temperature t and
A, as referred to a standard gas at the temperature T and
ire //, we have, as before,

Wi

if I? represent the density at t and h', referred to the standard at
nd //', r and Q, become

r l+at h % i+a'T II

~ T* and G TT"7?7'' 77"'

/i I +a 2 *2

a and a' being the coefficients of expansion of the gas and of the
.'.lard; consequently,

n-D— - l +at 1 + tt'y/

U"h' i+af l+a'T'

If we suppose the standard unchanged, those expressions be-
come, in the case of solids and liquids,

and in the case of gases,

which are obviously true, as they are merely the algebraic st
ments (69) of the fact, that when the standard is unaltered the
tabular density of a body varies directly as the weight «•!' a ^,
volume of the material of which it is composed.

As examples of the application of tlu-M- expressions, let it be

i«d to determine, first, the dmsity of mnvury at 15° C.,

in r. :o water at4°.i, b< ii; its density 13.598, in

• to water at o°.

/>- 13-598, Ar = o, ATV=.OOOI (by H.iUtriimV table),

& = o, gr = — 5_; then
555°

D '- 13.562.

'|llilV«l to drtrriliilH- tlir drllM;

nogen at 50° (\ and under tin- •>!' tuent v-ei^ht ineli<

108 APPLICATIONS OF THE LAWS OF DILATATION. [BOOK I.

mercury, its density being 1.8064 at o° and thirty inches, the den-
sity in both cases being referred to air at o° and thirty inches.

Here JD = 1.8064, A' =28, ^ = 30, a = .00387, £=o°, £'=50°;
therefore

D = 1.412.

7 1 . Connection of barometric Heights for Temperature. — In all
calculations in which the weight and pressure of the atmosphere
are regarded as proportional to the corresponding height of the
barometer, it is supposed that the column of mercury in the latter
has a constant temperature, as otherwise its weight will not be
simply proportional to its height, as it is assumed to be in such
calculations. In all accurate observations, therefore, it is necessary
to reduce the height of the barometric column to that which a
column of equal weight would have at some constant temperature.
To do this, suppose h to be the height of the column at the time
of observation, when the temperature is £°, and let H be the
height of a column of equal weight, at the standard temperature
T° ; then, as the volumes of the mercurial columns in the same
tube are proportional to their heights, we have

H i + ar

~h ~ i + & '

where §, the coefficient of the expansion of mercury for i° C.,
equals i -j- 5550. If T° = o° we have simply

11= h

555°

555° +

72. Connection of Measures of Length for Temperature. — In
determining the linear dimensions of bodies by the application of
a rule of known length, any error arising from alterations in the
latter from changes of temperature is, in ordinary cases, quite in-
appreciable. The errors, in fact, resulting from other sources,
chiefly from the inaccurate adjustment of the rule to the body
to be measured, far exceed any arising frorh expansion. When
the distance to be measured, however, is considerable, as in the
case of the base line of a trigonometrical survey, and extreme
care is taken to avoid other sources of error, then alterations in
the length of the rule by changes of temperature produce sensible

CHAP. I.] APPLICATIONS OF T1IK LAWS OF DILATATION'. 1 09

! s, which may be obviated cither by some mechanical contri-

vance for counteracting the expansion,* or by determining the

length of the rule when it is applied to the measurement of

a given portion of the line. This length is known immediately

from the formula,

if we know the corresponding temperature, t', and the length of

the rule, /,, at a known temperature, t. The difficulty in ap-

plying this formula consists in the determination of the true tem-

perature of the rule at the time of observation, for if we assume

mjHTuture to be the same as that of the atmosphere, as shown

by a delicate thermometer, then if the atmospheric temperature

undergoes sudden changes, the thermometer, on account of its

.-mailer nia.-s will be quicker in experiencing the corresponding

changes than the rule, and accordingly will not accurately indi-

the temperature of the latter. This difficulty may be obvi-

, by the following method, due to M. Borda, in which the rule

i- made its own thermometer.

Suppose, as in Fig. 20, two bars of metals of diil'ereiit expan-

red immoveably in a certain line, ef, at one extremity,

and free to move at the other. Let the standard length fnnu the

laid down on one of those bars, AB, when both !

-ame known temperature. which we will suppose to be o° C.

th b«' en, and draw •!/>•;/ parallel to the fixed lin,-.

• •rature of the bai> he raised to '/' , the teinpeiature

ter, and Mippose the upper bar to have gained the

CC on the lower, and let this distance he marked u\\ the

r, and divided into any number, in, oi'ecpial part>. Then

- easy, at any instant, to determine the true leng:h of the

'lie.- ea. For suppose at any time that the har AH has gained

.visions on the bur en, l.^th having the temperature (' ; then,

if those divisions were of invariable magnitude, the number

ruence --I' the rise of temperature t°, would be t-«

P° M tln^r temp. ,ul,l

Hiy see
.rasa U-odwy, ,,. 65.

I 10 APPLICATIONS OF THE LAWS OF DILATATION. [BOOK I.

have — = y ; but the actual length of the n divisions at t° is to

that of iliejn divisions at 7"°, in the ratio n(i + kt):m(i + kT), k
being the coefficient of expansion for 1° of the bar AB, on which
we have supposed the divisions traced ; therefore we have

m(i+kT)
which gives

n

m + (m - n)k T '

and therefore if L represent the length ea at o°, or the standard
length, its length at t°, when the upper rod has gained n divi-
sions, will be L ( i + kt), or

L(i+kT -?——].

\ m + (m- nVCJ. J

(ra

If k T, the coefficient of expansion of the bar AB for T°, be repre-
sented by the vulgar fraction -, the preceding expression may be
put under the form

<•*«-=

which expresses very simply the true length of the rule corres-
ponding to an advance of n divisions.

73. Effect of Change of Temperature on Measures of Time. —
Measures of time are also affected, as well as measures of length,
by changes of temperature ; for the immediate object of the in-
struments in general use as measures of time is to register the
number of vibrations made from a given epoch by some oscilla-
ting body, either a pendulum, as in the case of clocks, or a ba-
lance wheel, as in that of watches ; and it is on the supposition
that the duration of each vibration is a constant quantity, that
the number of such vibrations is assumed to measure the portion
of time which has elapsed from that epoch ; but we learn from
the principles of mechanics that the duration of the vibration of
an oscillating body depends on the distance of its particles from

CHAP. I.] APPLICATIONS OF THE LAWS OF DILATATION. I I I

the axis of suspension or centre of motion, and this distance being
affected by change of temperature, it follows that the duration
of the body's vibrations is affected by the same cause.

Jt has been shown by mathematicians that if a material point
is connected, by means of an inflexible rod devoid of weight, with
a horizontal axis of suspension, and oscillates in vacua in a vertical
plane, the duration of each vibration is independent of the mag-
nitude of the arc it describes, provided that this arc be very small,
and depends only on the force of gravity, and on the distance of
the moving point from the axis of suspension. To this abst
tion they have given the name of the i<h/ij>ti' j» minium. It is,
however, not only impossible to construct a pendulum exactly
fulfilling the above conditions, but it is not even possible in
practice to approach them nearly, for as all pendulums execute
their vibrations in air, a considerable mass must be given to them
to prevent their motion from being materially disturbed by the

•ance of that medium, and to secure inflexibility the parts

uniting the moving mass with the axis of suspension must ne-

rilv l>c possessed of considerable Strength and weight. They

• an analogy, however, to the simple pendulum in this re-
spect, that they generally consist of a mass of matter called the
bob, of considerable weight as compared with other parts of the.

.!-atus, and connected by a simple or compound rod with tin-
axis of su-prnHon. And tin- heavier the bob is in proportion to

rest of the apparatus, and the more condensed the in..
in it is, the more striking is this analogy, and the more nearly
«>(' this compound /n')t< hi Itttn, as it is called, in

-iti'.n t<. the afore-mentioned al»traction, isochronous with

6 of & si)/ '////////, whovr length is equal to the dist..

Of the hoh from the |

In t dcaeeif has hern shown that the vibrations of a

•>ound pendulum are isochronous with those of a simple prn-
duh, ML'th is equal to the (ju.'tient of the moment of

lift of the ice to it« axis of suspension, divided

1 3 statical moment with re-pert tO I Acc..rd-

LflBOfl of the IU0p6ndihg frame and
:its of inertia of the frame ami
bob round their resp. <

112 APPLICATIONS OF THE LAWS OF DILATATION. [BOOK I.

of those centres from the axis of suspension, and L the length ol'
the isochronous simple pendulum, we have

-S 7*7 TT\ - •

m C + mD

74. Principle of Correction. — The quantities mJ.2, m'Z?2, &c.,
are all functions of the weight and dimensions of the several parts
of which the pendulum is composed, and of the distances of their
centres of gravity from those of the frame and bob, and from the
axis of suspension. Now as all these dimensions and distances
are affected by change of temperature, it follows that the dura-
tion of the vibrations of the pendulum will be altered, unless there
is such a relation established between the various parts that the
changes of volume they experience shall counteract one another,
and the preceding value of L be thus retained unchanged. This
condition will be fulfilled if we give to the different parts of the
instrument values consistent with the equation which is obtained
by equating to cypher the variation of the preceding expression
forZ, arising from change of temperature; and as this variation is
always exceedingly small, we may obtain it by means of the or-
dinary rules of the differential calculus.

Without pursuing this investigation, however, it is easy to
see that we can, at least to a certain extent, fulfil the above con-
dition, if, by any mechanical contrivance, we can cause the dis-
tance of the centre of gravity of the frame or of the bob from the
axis of suspension, to remain unaltered, or rather slightly to di-
minish, while the other dimensions and distances are increased
by rise of temperature. And we will accordingly now proceed
to explain how this object has been sought to be effected, and
first will describe some of the methods devised for counteracting
the increase of the distance of the centre of gravity of the bob
from the axis by increase of temperature.

7 $ . Grahams Compensation Pendulum. — Mr. Graham , an Eng-
lish clockmaker, appears to have been the first who constructed
a pendulum in which this object was attained. The pendulum
which he proposed consisted of a rod of glass, to the extremity
of which was attached a cylindrical vessel containing a quantity
of mercury. As the rod expanded by heat, the centre of gravity

(-MAP. I.] APPLICATIONS OF THE LAWS OF DILATATION. I 13

of the mercury was lowered, but it was at the same time raised
by the expansion of the mercury itself, and if the lengths of the
i nd of the mercury were duly proportioned to their coefficients
of expansion, the distance of the centre of gravity from the axis of
nsion might not only be retained unaltered, but even dimi-
d by rise of temperature. Then let I be this distance at
any temperature £°, h the height of the cylinder of mercury at
iinc temperature, k and A the coefficients of expansion of the
nul of mercury in glass for i°, referred to the temperature £°,
then, for any rise of temperature r, the centre of gravity would be
lowered by the expansion of the rod by the quantity kr\ ; but
it would be raised by the expansion of the mercury, by the quan-
tity A - r, and accordingly, if those two quantities were equal,
that is, if

K-A*

the distance of the centre of gravity of the bob from the axis
would n.' main unaltered, and if the right hand member of the
equation were the greater, this distance would be diminished.

A pendulum of this description is represented in Fig. 40.

The correction to bring it to time at the mean temperature was

made by means of the weight d, which was capable of motion

: the rod; and the correction for imperfect compensation, by

• _: or diminishing the quantity of mercury in tin- jar. This

ment, however, was considered objectionable, as it altered

range of the index t on the arc of motion: and accordingly

| "ii.-truetion of the mercurial pendulum in I . in whirh

tion is regulated by a screw which raises and loweis

ifl that MOW generally adopted.

I '.I I icoC s Pendulum. — In the pendulum represented 1:

42, and which is constructed alter the plan Mi^'Med l>y Mr. Kl-

et«-d. The r..d AB consists of

bars, to one of which are attached two short levers, turning
• 'litres o, o', and acting at one extremity on the en

which i>

.eiitly M-n-wed to the ! • I), acts on the other extra

C of i US; and accordin ,. l>y the eilcct ol' in-

q

1 14 APPLICATIONS OF THE LAWS OF DILATATION. [BOOK I.

creased temperature, the first bar is elongated, and the bob de-
pressed, the second bar, expanding, acts on the end c of the
levers, and raises the bob by a quantity depending on the differ-
ence of expansion of the bars, and on the ratio of the arms of the le-
vers. The amount of correction may be very accurately regulated
by means of the screws a, a , the advancing or withdrawing of which
alters the ratio of the effective portion of the arms of the levers.
Let / represent the distance of the centre of the bob from the
axis of suspension at the temperature t°, k the coefficient of ex-
pansion of the main bar for i° referred to that temperature, I the
length of the compensating bar, and k' its coefficient, and m -=- n
the ratio expressing the effect of the levers ; then, in order that
the length I should remain unaltered, we should have

Ik . l(K- *)™.

77. Harrissoris Gridiron Pendulum. — The next form of com-
pensating pendulum to which we will direct the attention of the
student is the invention of Mr. Harrisson, and from its form is
usually called the gridiron pendulum. In this pendulum the bob
is suspended from a system of rods, some of which, by their con-
nexion, can only expand downwards, and others upwards, and
the lengths of the rods being so determined with reference to their
expansibility, that those expansions in opposite directions shall
mutually counteract each other, the centre of gravity of the bob
may be made to retain its distance from the axis unaltered. The
arrangement of the rods is shown in Fig. 43 : those shaded with
dark vertical lines represent rods of iron, those with the fainter
horizontal shading rods of brass or zinc, or some metal more ex-
pansible than iron. By the construction exhibited in the figure
it will be seen that the iron rods all depending from the cross
traverses can only expand downwards, while the others resting
on those traverses must expand upwards. It will also readily
appear, from examination of the figure, that if we denote by SX
the sum of the lengths of all the iron rods, and by SX' the sum
of the brass, and by I the distance of the centre of the bob from
the axis of suspension, we have

SX - 2X' = l\

CHAP. I.] APPLICATIONS OF THE LAWS OF DILATATION. I 15

but in order to maintain / invariable it is necessary that we should

*2A - A'SA' = o,

k and k' being the coefficients of expansion of iron and brass, for
i° referred to the temperature at which the lengths are estimated;
•rdingly we have

by means of which equation we can determine the length to give
the more expansible metal, in order to preserve the distance /
unaltered.

From the above equation it appears that a compensating pen-

dulum may be constructed on this plan with any two metals, for

which k' and k have different values ; if the difference between

1 quantities, however, is very small, the sum 2A' of the

lengths of the compensating bars must be very great, and as the

length of each of them must be less than /, their number in such

must be very considerable. In such case, also, the mass of

the frame is very large in proportion to that of the bob, and the

iulum deviates widely from the form of the simple pen-

dulum.

The correction for bringing the pendulum to time at the

i temperature is made by means of the screw d, while that

;n perfect compensation is effected by having one of the cross

, generally the last, capable of being shifted on the rods

to which it is attached, by which means the sum 2A' of the

tlis of the compensating bars is altered, and consequently the

amount of tin- variation in the distance / adjusted.

78. Compensation r<:n<lnlum with compound cross Bar. — In
last form of compensating pendulum which we will n,
the compensation i- « -fleeted by counteracting t he alteration in
of the centre of gravity of the frame, or rather of t lie
i centre ol 06 and 1mb, from the axis of su

It d M tin- principle, that if two metallic bars of diileivnt

:-ility are linnly secured to each :iy change of

iicraturc will cause such a system to warp or bend, the more

I 1 6 APPLICATIONS OF THE LAWS OF DILATATION. [BOOK I.

expansible bar forming the outside of the curve if the tempera-
ture is raised, and the less expansible if it is lowered. Accord-
ingly, if such a compound bar, having two balls, a, «', moveable on
screws attached to its extremities, is secured at right angles to
a pendulum rod, as in Fig. 44, with the more expansible metal
placed underneath, the effect of increase of temperature will be
to raise the centre of gravity of the two balls, a, a', and thus the
descent of the centre of the bob, owing to the same cause, may
be counteracted. The amount of the correction may be regu-
lated by moving the balls a, a' to or from the rod.

79. Compensation Balance in Watches. — In watches the regu-
lation of the movement is effected by a balance-wheel, to which
a vibratory motion is communicated by a spiral spring, alternately
closing and opening. If the length of the spring and dimensions
of the wheel be altered by change of temperature, the periods of
the vibrations will also be altered. A compensation of this al-
teration may be effected by forming the periphery of the wheel,
as in Fig. 45, of two compound bars similar to that last described,
loaded with small screws. The effect of a change of temperature
will be to move those screws nearer to the centre or farther
from it ; in the first case a smaller force will be necessary to effect
the vibratory movement, in the latter a greater. And the po-
sition of the screws may be so arranged as to counteract the effect
of change of temperature in altering the force of the spiral spring
and the dimensions of the wheel.

80. Pyrometers. Wedgwood's Pyrometer. — Instruments des-
tined for the measure of high temperatures are called pyrometers ;
these are constructed either of refractory solids, or of air contained
in a refractory envelope. Wedgwood proposed a pyrometer formed
of clay cylinders, which, contrary to the general analogy, contract
on being exposed to high temperatures. Their diameter was mea-
sured by a gauge formed of two converging rules, before and
after they had been exposed to the temperature to be estimated,
and their change of volume was supposed to bear a fixed relation
to the change of temperature to which they had been submitted.
It has been ascertained, however, that their contraction, which is
due to loss of moisture, is influenced by the length of time to which

CHAP. I.] APPLICATIONS OF THE LAWS OF DILATATION, 1 17

thev are exposed to a given temperature; and that exposure for
:ig time to a lower temperature produces as great a contrac-
tion as for a shorter time to a higher.

81. Gwjton •nil's Pyrometer. — In the year 1803 M.
•on do Morvcau* published a description of a pyrometer com-
posed of a bar of platina 45 millimetres long, 5mm broad, and 2mm
thick, which was placed in a groove sunk in a slab of well-baked
porcelain. The bar pressed at one end against the extremity of
the groove, and at the other against the shorter arm of a platina
lever 2.5 millimetres in length, whose longer arm, 50 millimetres

.-. traversed a graduated arc, also of platina, which, by means
of a vernier, was capable of being read off to the one-tenth of a
degree. The expansion of the platina bar, calculated from the

1 escribed by the end of the longer arm of the lever, served to
measure the temperature to which the apparatus was exposed.
As it appears, however, that platina softens at high temperatures,
it is probable that the motion of the index arm round its centre

along its scale would be impeded by this cause, and that the
indications of this instrument, accordingly, at high temperatures,
could not be safely relied upon.

82. Dan rometer. — In this respect the apparatus em-
ploy- ' . Daniell (see p. 31) for the measurement of expan-
sions, and which may also be employed as a pyrometer, possesses
a considerable advantage, as its scale is not exposed to any change
of temperature. When used as a pyrometer this instrument is
furnished with a platina or iron rod, whose expansions, d«
mined by means of the scale, indicate tin- corresponding cha:

mpcrature. If it is de.-in-d t<> compare the indications ». I' this

;it with those of a nn-rciirial ur air therm- >; .<! to

nuke its degrees identical with those of the latter in.-ti nment, a

nation is obtained by suppi^'mi: tin- rate ol'e.xpan
of platina or iron the same as that of air <>r mnvurv in ;jla— en-
velopes. Then, knowing the expansion of th ds for a gi
.re, as measured on the mercurial or air therm, .m
ft Simple pr<-]< the temperature, calculated according

. p. 276. Memoires <1< 1 i
tontix. (1808), t

n8

APPLICATIONS OF THE LAWS OF DILATATION- [BOOK I.

to the same scale, corresponding to an observed expansion of the
metal in the register. Thus having ascertained that an expansion
amounting to .0152 corresponds to a change of temperature of
600° F., we obtain the temperature corresponding to the expan-
sion .0508 by the proportion

.0152 : .0508 :: 600° : 2005°.

In this way the following table has been obtained by Mr. Da-
niell.

TABLE of the fusing Points of the Metals enumerated (Temperature
at Time of Observation being 65° F.)

Metals.

Bar in
Register.

Expansion
for 600° F.

Expansion
observed.

Temperature.

Copper fused,

Platina,

.0152

.0508

2005° + 65 = 2070°

Gold do.

Do.

.0159

•°537

2026 + 65 = 2091

Do. do.

Iron,

.0229

.0787

2061 +65 = 2126

Silver do.

Platina,

.OIl6

•0363

1877 + 65 = 1942

Do. do.

Iron,

.0203

.0645

1906 +65= 1971

Iron do.

Platina,

.OIl6

.0546

2824 +65 = 2889

Zinc do.

Iron,

.0203

.0239

708 +65= 773

Do. inflamed,

Do.

.0245

.0358

876 +65= 941

83. Air Pyrometer. — The expansion of air may be employed
to measure changes of temperature, through a very considerable
range, by means of the apparatus represented in Figs. 36, 37,
38, 39, and described in (53), (54). The ball A may be made of
glass for ordinary temperatures, but for very high temperatures,
when the instrument is used as a pyrometer, a ball of platina is
required. The coefficient of expansion of air being known, the
equations in pages 86, 88, give the temperature corresponding
to an observed expansion.*

84. Breguefs metallic Thermometer. — A very sensitive metallic
thermometer has been constructed by M. Breguet for ascertaining
changes of atmospheric temperature. It consists (Fig. 46) of
a cylindrical spiral formed of three metals, silver, gold, and pla-

* See also Pouillet, Elements cle Physique, vol. i. p. 253 (4™ Edition).

THAI'. I.j APPLICATIONS OF THE LAWS OF DILATATION. I Ip

tina, superposed, and rolled out until their joint thickness does
not exceed one-sixtieth part of a millimetre, or .000656 inch. Its
mass being so small, the least change of atmospheric temperature
immediately affects it, and, owing to the different expansibility
of the silver and platina it coils and uncoils, carrying an index
;le round an arc graduated by comparison with a delicate
mercurial thermometer. The whole apparatus is enclosed within
a glass case, to preserve it from external causes of disturbance.

A different form of this instrument is represented in Fig. 47,
where the apparatus is enclosed in a case similar to that of a com-
mon watch. The thermometric bar, ab, acts on one end of a lever,
-e other end carries a rack which gives motion to the pinion
to which the index, erf, is attached. A spiral spring, A, serves to
bring back the index and lever when the bar returns to its origi-
nal position.

85. Force of Contraction and Expansion of Metals. — The force
which a metallic bar exerts at any instant in the direction of its

;h, when contracting on change of temperature, is equal to
the force which would be necessary to extend it, at its tempera-
ture at that instant, by a quantity equal to the amount of contrac-
tion. Thus a bar cooling from 81° F. to 80° F. exerts a force
equal to that which would be required to extend it at tin- tempe-
rature of 80° F. by a quantity equal to its contraction from 81°
to 80°. The only experiments on the laws of tension of metallic

with which we arc acquainted are those made in the ca-
malleable iron, and at the ordinary temperatures. l»v Mr. I

•rding to this author, a bar of malleable iron is extended
about I -•- looooth part of its length l»y a weight of one t<>n per
square inch of section, and the elastic or restitutive Imve is tret-

<1 or destroyed by a weight of ten tons per inch, or an < •xtm-
i of i -f- loooth part of the length. SuppoHiiLr tin-si- values

•Id good, as they probaMy <!». within the limits ufatmnsjOu--
iires of temperature, it is easy to calculate the i

. hen contracting on any ehuiiL'e i.f temperature
within tho.-r limits. For as wrought ir<>n • i -j- looooth

•Mn-n^tli «.f M

120 APPLICATIONS OF THE LAWS OF DILATATION. [BOOK I.

of its length at th«' mean temperature, for a change equal q. p.
to IS°25 F., it follows that a bar whose temperature is origi-
nally I5°25 F. above the mean, s» rurcd at its extremities to
points maintained at an invariable distance, tends to draw its
supports together by a force equal to one ton for each square
inch of its section, on cooling down to the mean temperature ;
for a change of 3O°5 F. its force of traction would equal two tons
per square inch ; and so on, within the limits above referred to.
Calling, therefore, t'° the higher temperature, t° the mean, and s
on of the bar in square inches, the force of traction T may
be expressed by

t-t

T = S - — .
15.25

Admitting, therefore, 76° F. to be the extreme range of tempe-
rature in tliis elimate, it follows that a bar permanently fixed at
tin- lii-jlu'.-t limit to supports maintained at an invariable distance,
would be subjected, at the lower limit, to a strain of five tons per
square inch of section, or one-half of that which it could bear
without the destruction of its elastic force. If the above law
held as far as 212° F., a bar fixed at that temperature would lose

tstic force altogether on cooling down to 60° F.
A familiar instance of the application of the contractile force
of wrought iron when cooling is exhibited in the mode of securing
the tires on wheels. The tires being made red hot, and thus
considerably expanded, are dropped over the periphery of the
wheel, and then cooled. If the wheel be of cast metal, the tire,
n cold, embraces it with such force as to render its removal
a matter of extreme difficulty. Care must, of course, be taken
not to make the tire too small, as it might in that case be ex-
posed, when cold, to a permanent strain, which would greatly
weaken its cohesion, and render it liable to fracture. If the
wh»'el l)c of wood, the contraction of the tire not only secures
itself upon the. rim, but also presses home the joints of the spokes
in th<' felloes and nave, and holds all secure. If r, as before, ex-
presses the contractile force in tons, the normal force on any small

portion <1a of the circumference will be r — , r being the radius

< HAP. I.] APPLICATIONS OF THK LAWS OF DILATATION. 121

ic wheel ; and therefore the force over the whole periphery
will be equal to ZTTT, w being the ratio of the circumference of a
circle to its diameter; and the felloes in the interval between the
spokes being supposed inflexible, the pressure p in the direction
of the spokes forming any diameter may amount to

t' -t

n being the number of spokes, t in this expression represents the
temperature at which the tire just fits the rim, and s, as before,
the urea of the section of the tire.

An ingenious application of this force was also made in the
case of a gallery in the Conservatoire des Arts et Metiers in Paris,
whusc walls were forced outwards by some horizontal pressure.
To draw them together, M. Molard, formerly Director of the
'urn in that establishment, had iron bars passed across the
building, and through large plates of metal bearing on a con-
siderable surface of the external walls. The ends of these bars
were formed into screws, and provided with nuts, which were
first screwed close home against the plates. Each alternate bar
then elongated by means of the heat of oil lamps suspended
from it, and when expanded the nuts were again screwed home.
The lamps being removed, the bars contracted, and in doing so

the walls together. The other set of bars was then
]>;mded in the same manner, their nuts screwed home, ami the
wall drawn in through an additional space by their com
. And this series of operations was repeated until tin- walls

• completely iv.-toivd to the vertical, in whirh position the
bars then serve.! permanently to secure them.

':h which a metallic, bar expands is in like man-

• ••jual to tin- force which would compress it through a space
:1 to that by whirh it is elongated. It appears from Mr i

low's experiments, that iii bars of malleable iron, when <leil«

depth of triiH.ui hears to the depth of cMiipre-ion a latio

l-'rom this it follow-, that the ;

i''1'!' presfl tin- ! through a small .-pace bears

to tl .'••piired • i it thmu^h the

The i;
R

122 APPLICATION n: LAWS OF DILATATION. [BOOK I.

hv he;it appears, therefore, to be considerably greater
than that arising from their contraction, but it is, for many rea-

iianageable, and less capable of practical application.
86. Allowance to be made for Contraction and Expansion of

/ — The force of the expansion and contraction of
metals being so considerable, allowance must be made for it in all
works in which large masses are united together, as otherwise
distortions of shape, or even destruction of part of the work,
might result. On railroads, accordingly, an interval should be
left between the rails when they are being laid, the amount of which
should depend on their temperature at the time, on the change
of temperature to which they will probably be exposed, and on the
length of the rail. Thus if L be the known length of the rail at
a given temperature t, L' its length at the temperature t at which
it is laid, and L" its length at the temperature 2", the highest to
which it will be exposed, then an interval equal to L" -L' must
be left between the rails when being laid ; but we have (36)

TH T i+kt" TI '

L = L - r-, and L =L

- r-, - T-,

i + kt i+kt

if k be the coefficient of dilatation of wrought iron for i°; there-
fore,

and if k be expressed by the vulgar fraction -, the interval i is

given by the formula

t"-t'

n + t

In long systems of gas or water pipes provision must also be
made for the effects of contraction and expansion. " When iron
water pipes were first adopted, it was the practice to make a flanch
at each end, for the purpose of connecting them together by screw
bolts and nuts; however, a little experience demonstrated the
inconvenience of this mode of constructing them, for the expan-
sion and contraction by the variations of temperature occasioned
their joinings cither to become loose and leaky, or the breaking

P. I.] APPLICATIONS OF THE LAWS OF DILATATION. 123

The various injurious effects and disadvantages
proceed HILT from this cause led to an alteration in their i'orm,
which proved an effectual preventive of any defects from the
n of heat and cold upon the metal. This important improve-
ment consisted in forming one end of each pipe larger than the

•r, with a kind of socket several inches in length, into which
the narrow end of the corresponding pipe could be inserted, and
the space remaining between them closely filled up with hemp
wadding and lead, so as to render the joining perfectly water-
tight. By adopting this method of connecting the pipes, the
changes of temperature have not the effect of breaking them,
though occasionally their joinings become imperfect, and require
a little repairing to prevent the escape of water."*

87. Effects of Expansion and Contraction on arched Bridges. —
/ iron bridges, which must bear against their abutments,
no room, of course, can be left for expansion in the direction of the
chord of the arch ; the effect of increase of temperature in such
structures, accordingly, is exhibited in a rise in the crown, which,
however, in ordinary cases, is so small in amount, as not to ex-
ceed the limits which the elasticity of iron admits of without

_rer of fracture. Thus, in one of the arches of Southwark bridge.
for which the length of the chord of extrados is 246 ieet. and its
versed sine 23 feet i inch, and accordingly the length of the arch,
gmentof a circle, 3020.8 inches, the rise- in the crown
of the arch for a change of temperature of i° F. was observed l>v
Mr. R< nniet to be about one-fortieth of an inch ; for 50° 1 .
accordingly, it would amount to about 1.25 inch. In Btone
bridges of se vend arches, th<- riled of the contraction prod;.

by cold is pcrrrivrd in the (.penini: o(' the joints of their par::
• of the a; -sion over the CTO1

while tli :<>n due to heat is exhibited, on the contrary, by

of the joints over the crowns. Instances of tl
noticed l>v M; . I!- nnie, in tin- case of t lie l>ri<:
I :ues at Stainc-. in the yea vihcd in the

d to.

'.Her- < ixii

ndon, fcc., by William Mat- Engineers, vol. iii. p. aoi.
thews, p. 70.

1 24 APPLICATIONS OF THE LAWS OF DILATATION. [BOOK I.

88. Alluicanct' to be made for Expansion and Contraction in
the case of tubular and Lattice Bridges. — In tubular and lattice iron
bridges, however, in which such alteration of form is inadmissi-
ble, a space must be left at either end to admit of the expansion
and contraction due to the change of temperature to which they
will be exposed, and some provision also must be made, especially
it' their weight is very considerable, to facilitate, by some form of
friction rollers,* the sliding motion of the free extremity, as other-
wise the support at that end might be shaken or destroyed. The
expression

. Tt"-t'

^ = L ,

n + t

in which L is the length of the bridge at any temperature t, and
t", t' the highest and lowest temperatures to which it will be ex-
posed, gives the value of the interval through which the free
extremity must be at liberty to move.

89. Effects of unequal Expansion and Contraction in Machines.
— In machines, and also in all large works of construction, in
which the parts form a strictly rigid system, care must be taken
as to the manner in which materials are combined, whose rates
of expansion are very different, so as to secure, in the former
case, the requisite freedom of motion, and in both to prevent the
distortion of form which might result from neglect of this precau-
tion. Thus if the socket, in the case of a stop-cock placed on a
cast metal pipe destined to convey water at different tempera-
tures, were made of cast metal, and the moveable part of brass,
the unequal expansion of the two metals would either produce
the effect of wedging it so tightly at the higher temperature as
to prevent all power of opening or closing it, or if it moved freely
at that temperature, it would be so loose at the lower as to leak,
and allow the water to escape.

It is probably in a similar way that the iron axles of heavily
laden goods' waggons on railways, when there is a failure in the
Mipply of the lubricating material, become wedged in their jour-
nals by the effect of unequal expansion, and are sometimes vio-
lently twisted, or even wrenched off.

* Civil Engineers' and Architects' Journal, vol. xi. p. 161.

CHAP. I.] APPLICATIONS OF THE LAWS OF DILATATION. 1 2

90. Effects of Chanye of Temperature on Buildimj*. — In the
case of buildings, however, although the rates of expansion of
some of the materials used in their construction differ as widely
as those of any two metals, yet the total amount of the diffe-
rence is so small as not to produce any sensible effect, where ab-
solute rigidity does not exist, and where there is the least room
for compression and extension. Thus Mr. Adie observes : ** From
the results given in the table it is evident that no danger is to
be apprehended from a change of temperature affecting cast in>n
and sandstone in a very different degree, as their expansion, in
so far as regards all building operations at least, may be regarded
•lie same. The difference between the expansion of bricks
and malleable iron amounts only to .00042 for 90° F., or half an
inch on 100 feet; and Roman cement, when in as damp a state

\\ buildings must be, will expand more than malleable iron,
since it did so in my experiment, even after it had been dried
for eleven hours at a temperature of 207°. This, therefore, will
in a great measure serve for an explanation of the fact men-
tioned by Mr. Brunei, in describing his method of constructing
arches, by suspending the courses of brick with straps of hoop-
iron, viz., that he hud hud some anxiety as to the manner in which
variations of temperature would affect his mode of operating, by

inding the metal more than the brick and mortar; but on
examining his experimental arch, both in summer and in wintrr.
not a crack was to be seen."*

* Transactions of the Royal Society of Edinburgh, vul. xiii. p. 367.

126 LIQUEFACTION AND SOLIDIFICATION. [BOOK I.

CHAPTER II.

ON THE RELATION BETWEEN THE TEMPERATURE AND THE STATE
OF BODIES, AND ON THE LAWS OF VAPOURS.

SECT. I. — LIQUEFACTION AND SOLIDIFICATION.

9 1 . Solidity dependent on Temperature. — Observation and ex-
periment prove to us in the case of all bodies, except the diamond
and charcoal, that their existence in the solid or liquid state de-
pends on their temperature. The point at which the change from
one of these states to the other takes place varies considerably in
different cases. The ordinary vicissitudes of atmospheric tempe-
rature suffice to produce it in some bodies, as water and oil ; the
alloys called fusible metals melt at temperatures near that of
boiling water ; tin, bismuth, and lead, are liquefied below a red
heat ; silver may be melted in a common fire urged by a bellows,
gold and copper in a wind furnace, and iron has been melted in
a small quantity in a draught furnace.

The most intense heat, however, capable of being produced
in the best furnaces, fails to affect platina. This metal, however,
yields to the heat of the oxy-hydrogen blow-pipe, and to that
generated between the poles of a powerful galvanic battery. By
means of the former apparatus Dr. Clarke reduced 100 grains of
platina to a state of fusion, and kept it liquid for some minutes.
Iridium is also melted in small globules by the same powerful
sources of heat, as also lime, magnesia, and silica.

There are some substances, again, whose fusion cannot be ef-
fected unless they are operated on under great pressure. This is
owing to their extreme volatility in the liquid form, which causes
them to pass directly, as it were, from the solid to the gaseous
state, under the ordinary atmospheric pressure. Thus Sir James

CHAP. II.] LIQUEFACTION AND SOLIDIFICATION. 127

Hull succeeded in melting chalk (carbonate of lime) confined in

gun barrel, under the of the atmosphere of

<>nic acid gas, disengaged by the action of heat, and converted

this means into crystalline marble.

Carbon, it has been observed, whether under the form of dia-
mond or of charcoal, has never been fused. When exposed to
high temperatures in contact with oxygen, this substance under-
goes combustion. Messrs. Hare and Silliman, indeed, announced
that they had melted charcoal in small globules between the
poles of a peculiar form of galvanic battery with large surf-
called a deflagrator; but there is no doubt that those globules
consisted, not of molten charcoal, but of some of the earthy bo-
dies from which, in its purest state, charcoal is never entirely
free. The diamond, when placed in vacuo, or in an atmosphere
of carbonic acid, and exposed to the action of the sun's rays con-
centrated by a powerful lens, in some instances becomes black
and carbonaceous, and acquires the property of marking the
fingers or paper.

M. Jacquelain has recently shown that the same result follows
from the action of a powerful galvanic battery. On placin
diamond between the poles of one of Bunsen's batteries, consist-
ing of i oo couples, "it became luminous, softened (se

i, acquired the property of conducting electricity (which tin;
diamond does not possess), and passed into the state of genuine
coke. Its density at the same time changed from 3.336 to
-8.- _

re is no doubt, however, that carbon, under its various

resents only an apparent exception to the general law that

all things are capable of being melted by "fervent h.-at ;" and that,

if it • 1 on under the circumstances required by

its chemical constin. .posed to a temp -ufli-

hi-jli, it would be reduced to tlie liquid state. \V.

. to consider some of the ]>hen«>n anted l»v

. hen passing from the s. .lid to the liquid state, and c.-n-

the former, as being in soinr
'Icr.

3"« Scric, tome xx. p. 467.

128

LIQUEFACTION AND SOLIDIFICATION.

[BOOK i.

92. Phenomena accompanying Liquefaction. — When heat is
applied to a solid body its temperature is raised, and continues to
increase gradually and constantly, until a certain point is attained,
when a change in its state commences; the temperature then

M>3 to rise, and remains unaltered until the change is com-
pleted.

The first point to be noticed in respect to the change from
the solid to the liquid state is, that it always takes place at a fixed
temperature for the same body; a temperature which, as has been
stated, remains unaltered until the whole of the solid mass has
been reduced to the fluid state.

M. Pouillet gives the following table of the point of fusion
of various substances, estimated according to the centigrade scale.

TABLE of the Fusing Point of various Substances, in Centigrade

Degrees.

Substance.

Fusing Point.

Substance.

Fusing Point.

English wrought iron,
French soft iron, . .

Qfppl

I600°
1500
1400 to 1 300

i atom lead, 4 tin, 5

n8°.9
114

107

IOO
TOO

94
90

58
43
70
68
61
55 to 60
49 to 43
49
45
33-33

0.0
- 10

-39

I25OtOlO5O

1250
1180

IOOO

900

432

360

320
262
230

Gold (pure), ....
Gold (in coin), . . .
Silver (pure), ....
Bronze • • ...

2 lead, 3 tin, 5 bis-

5 lead, 3 tin, 8 bis-

4 bismuth, i lead, i

Lead ....

Sodium,

liismuth . .

Tin

Stearic Acid, ....

5 atoms tin, i lead, .
4 tin, lead, ....
3 tin, lead, ....
2 tin, lead, ....
I tin, lead, ....
i tin, lead, ....
3 tin, bismuth, . .
2 tin, bismuth. . .
i tin, bismuth, . .

194
189

186
196
241
289

200
167.7
I4I.2

Wax (bleached), . .
Wax (unbleached), .
Margaric acid, . . .

Spermaceti,

Tallow

Ice

! Oil of turpentine, . .

. Il] LIQUEFACTION AND SOLIDIFICATION. 1 29

M. Pouillet* states that he determined all the preceding fusing

its above the temperature of a red heat, about 500° C., either
l»v means of his air pyrometer, by the method of specific heats, or
by the help of a magnetic pyrometer, described in the second
volume of his " Elements de Physique."

The second point of importance in reference to the phenome-
non of liquefaction is, that a considerable quantity of heat is

; bed by a body during this process, which produces no change
in its temperature. In ordinary cases of fusion by heat this
quantity is supplied by the source of heat, but if fusion is effected
by chemical action, as in the mixture of salt and snow, or pounded

and other combinations which will be mentioned hereafter,
this supply of heat is taken from the mixture itself, and from

•unding bodies, which are thus considerably reduced in tem-

ture. The quantity of heat thus absorbed, as it produces no

t on the temperature of the melting body, which remains, as

mentioned before, at a constant temperature during the
whole process of liquefaction, is called latent heat; and as it is

ssary to the existence of the body in its liquefied state, it is
railed the constituent heat, or caloric of liquidity of the fluid.
The fuller consideration of the subject of latent heat i

ed for the second chapter of Book 1 1 .

93. Phenomena accowj v »//»////'/•/*//,///. — The return from

the liquid to the solid Mali1 takes place at the same temperature

at at which tlu? change from the solid to the liquid occur-.

cases, indeed, liquids may be reduced below this point,

and .-till retain their fluid state. Thus water, deprived of air by

nt hoiling, and slowly cooled, may be reduced to - 6° C.,
without conflation ; and if it is enclosed in a tube where it is

•sedonly to the pressure of highly raivlied air, and its sin

is covered with a thin lilm of oil, it may even be reduced to

('. ; the presence, however, under those circum-tances, of

the smallest fragment of ice, or the least vibratory movement, im-

med its solidiiication, on which its temperature

C . \Vat<T ••MMtaiiunLT c:«rl)"nie acid al\vay«

' Elements de Physique, vol. i. p. 299.
8

130 LIQUEFACTION AND SOLIDIFICATION. [BOOK I.

congeals at o° ; the same is the case also with water which is
at all turbid. It appears that the temperature to which it can
be cooled below o°, without congelation, is so much lower the
smaller the diameter of the tube is in which it is contained.
This may assist in explaining the fact, that the water contained
in plants is not frozen except at very low temperatures.

As absorption of heat takes place during liquefaction, so a
disengagement of it is effected on returning to the solid state.
If it were not for this, the process of solidification would be in-
stantaneous, and would take place the moment the fluid mass
reached the temperature of liquefaction of the solid. But in
consequence of this disengagement of heat, whenever a small
portion of the superficial film of the liquid, which is probably
below o°, is solidified, the temperature of the surrounding parti-
cles is slightly raised, and must again be lowered before their
solidification can take place.

As there are some solids which, as has been mentioned, have
not been reduced to the liquid state, so, on the other hand, there
are some liquids which no degree of cold yet attained has solidi-
fied. Among these are ether, alcohol, sulphuret of carbon, cam-
phine, or rectified oil of turpentine, caoutchoucine, and several
of the liquefied gases. These liquids, when submitted by Mr. Fa-
raday* to a temperature of - 166° F., still retained their liquid
state, although alcohol, camphine, and caoutchoucine lost some-
what of their fluidity, and became thick like oil.

94. Abrupt Change of Volume accompanying these Changes of
State. — Most fluids, on assuming the solid state, undergo an ab-
rupt change of volume. In the case of mercury contraction takes
place ; in the case of water, cast iron, and bismuth, on the con-
trary, there is considerable expansion. The sudden contraction
of mercury is strikingly exhibited by solidifying this metal in a
mercurial thermometer. As the temperature is lowered, the mer-
cury falls until it reaches - 39° C., where it remains stationary
for a^considerable time, and then suddenly sinks to a point which
would mark about - 300° C. This phenomenon led early ex-

* Philosophical Transactions, 1 845.

CHAP. II.] VAPORIZATION AND LIQUEFACTION. 1 ^1

re not acquainted with its cause, to assign

t.-mperature of- 300° as the freezing point of mercury. Its

or, was ascertained, and the true freezing point of

mercury fixed at- 39°, by a series of experiments made by Mr.

Ilutchins at Hudson's Bay, in the winter of 1781, under the di-

.13 ut' Mr. Cavendish.*

The sudden contraction of mercury on assuming the solid

unts to about one-twenty-third of its volume at its' freezing

point. The expansion of water, under the same circumstances,

uch greater, being 0.07 of its volume at o°. The force with

which this expansion is effected is very considerable. Major

Williams, during a severe winter at Quebec, rilled a mortar with

r, and closed its muzzle with a plug of wood driven home

with a sledge-hammer, the temperature of the surrounding air

being at - 28° C. After awhile the water was frozen, and the

•quent expansion took place with such force as to project the

wood, with a loud explosion, to the distance of 400 feet. The

effect of the expansion of water in freezing is also exhibited in

severe winters, by the fracture of rocks in whose crevices water

has lodged, and in the loosening of considerable masses from high

cliffs, owing to the same cause. It is to this expansion also that

the injurious effect of frost on plants is due, since, when the water

tinrd in the capillary tubes of which they are composed is

n, its expansion breaks up their envelopes, and entirely de-

ir organization.

A reference to M. Despretz's Table in p. 63 will show the
its of congelation of different saline solutions, and their t«-m-
while tli is change is taking place.

SECT. II. — VAPORIZATION AND LIQUEFACTION.

Definition and Measure of tJie Tension or elastic 1
,<we*. — The essential difference between the ,-,>lid. liquid, and
gaseous states coi. the physical connexion between the

• states. In -olid

* I'lnl'-.-i-hi. .il Transactions, \. I. l\.\iii. 1783.

132 VAPORIZATION AND LIQUEFACTION. [BOOK I.

particles LUC held together by a strong attractive force which
powerfully resists their separation ; as their temperature increases
this force diminishes, very gradually indeed, and almost insen-
sibly at first, but more rapidly as the point of fusion is ap-
proached, as is strikingly exemplified in the case of metals. In
liquid bodies this attractive force almost entirely disappears, and
the constituent particles of fluids possess a freedom of motion
inter se, which is the more perfect the more nearly the state of
the body approaches to that of perfect fluidity ; while in gaseous
bodies the particles appear endowed with a mutually repulsive
force, which causes them to separate from one another, and tends
to produce an almost indefinite enlargement of volume. In order
to exist, therefore, in a limited space, a gas must be contained in
a vessel enclosed in all directions, against the sides of which the
repulsive action of its particles causes it to exert a pressure, which
is called the tension or elastic force of the gas. The amount of
this pressure on any given portion, as for instance on the unit of
surface, may be represented by the weight which would retain
that portion of the enclosing vessel in its place if it were detached
from the remainder ; or the elastic force of a gas, without any refe-
rence to the extent of surface on which it acts, may be expressed
by the height of a mercurial column, at a given temperature,
which it would support, as this height is independent of its sec-
tion, or of the surface on which the gas may exert its pressure.
To illustrate these methods of expressing the elastic force or
tension of a gas, imagine a hollow cylinder, the area of whose
section equals a square inch, closed above and below, and fur-
nished with a moveable diaphragm or piston. Below this piston
suppose the space in the cylinder occupied by a gas, and above
it imagine a perfect vacuum. If the diaphragm were devoid of
weight the repulsive force of the particles of the gas would drive
the piston to the upper part of the cylinder, and the gas would
occupy it entirely; but if the piston were either itself sufficiently
heavy, or were loaded to a sufficient amount, the gas would be
i < -turned in a limited space, and its elastic force, under any given
circumstances of temperature and density, might be expressed by
the weight which it supported on a square inch of surface, in the

< HAP. II.] VAPORIZATION AND LIQUEFACT! 133

present case, the weight of the piston and its load. This weight,
under the circumstances supposed, might be of any amount, how-
ill ; but if the upper cover of the cylinder were removed,
and the surface of the piston exposed to the atmosphere, it could
not be less than the weight of the piston + that of the atmosphere
on its surface.

To understand the second method of expressing the elastic
force of a gas, conceive a U-shaped barometer tube, closed at both
ends, and containing a quantity of mercury in the lower or curved

. Imagine the space over the mercury in one arm a vacuum,
and that in the other filled with a gas. The latter will exert a

-sure on the surface of the mercury in contact with it, and
will accordingly depress it, and raise the column in the other arm.
The difference between the heights of the two columns will mea-
sure the elastic force of the gas, and the amount of its pressure
on any surface will be equal to the weight of a column of mer-
cury whose height equals this difference, and the area of whose
section equals that of the given surface.

96. Division of Gases into permanent Gases and Vapours. —
Gases are divided into the two classes of permanent gases and /•<«-
pours. The former were originally so called under the imp
sion that they existed permanently in the gaseous state, and could
not be possibly reduced to the liquid form ; while those which
could be so reduced, and could be reconverted to the stat<
gas, were called vapours. Sir H. Davy and Mr. Faraday,* how-
, have shown that by the conjoined effects of great prc>-

; hii/h degree of cold most of the permanent irases
be li Tin- pressure was produced either, as Sir H.I1

suggested, by generating the gas in large quantities in a limited
space, and thus making its own tension produce tin i

-are, or by means of a powerful eondi'n.-ini: pump. The

1 was produced in Mr. Faraday 's later experiments by means

of a mixture «•{' solid carbonic acid and ether. 1-W the purpose

the degree of c<»ld pr<>due«'d l,v this means, Mr.

lay rni] -pint thermometer, whose scale he gradu-

l.el..\v 1- . on the Mip; of a unit. of OOH-

* I'liil'-",.!,,, all'ransactioiw. i'-:;. M. "'• . ll

134 VAPORIZATION AND LIQUEFACTION. [BOOK I.

traction with the mercurial thermometer. He thus estimated the
temperature of this mixture at - 1 06° F. in air ; on placing it,
however, under the receiver of an air pump, and drawing off the
air and vapour of the carbonic acid, the temperature fell to - 1 66°
F., and at this point the vapour had only a tension equal to 1.2
inch of mercury, and accordingly the mixture of acid and ether
was not more volatile than water at 86° F., or alcohol at the or-
dinary temperature.

By these means Mr. Faraday succeeded in liquefying all the
permanent gases except those undermentioned, which at the sub-
joined temperatures and pressures still retained the gaseous state.

Hydrogen at - 166° F. and 27 atmospheres.

Oxygen, „ - 166 ,,27 „

Do. „ - 140 „ 58.5 „

Nitrogen, „ - 166 „ 50 „

Nitric oxide, „ - 166 „ 50 „

Carbonic oxide, „ - 166 „ 40 ,,

Coal gas, „ - 166 „ 32 „

Several of the liquefied gases are further capable of being
reduced to the solid state. Thus, hydriodic acid passes from the
solid to the liquid state at - 60° F. ; hydrobromic at - 1 24° ; sul-
phurous acid at - 105°; sulphuretted hydrogen at - 122°; carbo-
nic acid at - 148°, according to M. Thilorier,* who first effected
its solidification; at from - 72° to - 70°, according to Mr. Fara-
day, at which temperature, whether in the solid or liquid state,
it exerts a pressure of 5.33 atmospheres; oxide of chlorine at
- 75° ; protoxide of azote at - 150° ; cyanogen at - 30° ; and am-
monia at - 103°; but olefiant gas, fluosilicic acid, phosphuretted
hydrogen, fluoboric acid, muriatic acid, and arseniuretted hydro-
gen, remain fluid at - 166° F.

The difference, then, between the permanent gases and va-
pours, is merely one of degree, and depends upon the temperature
at which the change from the fluid to the gaseous state occurs.
Those which exist in the fluid state under ordinary temperatures
and pressures are called vapours, while those which require

* Anuales de Chimic ct de Physique, tome ix. (1835).

rilAl'. II.] VAPORIZATION AND LIQUEFACTION. 135

strong pressure and high degrees of cold to reduce them to the
liquid form are called permanent gases.

between elastic Force and Density; Boyle's and
iottes Law. — Towards the close of the seventeenth century
it was announced by the Hon. Mr. Boyle,* that the spring of
pressed air is directly proportional to the amount of its com-
-ion ; in other words, that its elastic force is directly propor-
.d to its density, or inversely to the volume occupied by the
mass at the same temperature. Thus if air occupying a
volume Vn sustains a pressure P0, twice this pressure will com-
» it into one-half of the original volume, three times the pres-
sure into one-third of the volume, and so on ; and conversely,
the same mass of air at the same temperature, occupying one-half,
one-third, &c., of its original volume, will sustain twice, thrice,
its original pressure. Mr. Boyle performed his experiments
with a U-shaped glass tube, whose arms were of unequal length.
In the shorter arm, which was closed at the extremity, was con-
tained the air on which he was operating; the longer arm, which
was open at the end, contained the column of mercury that pro-
'1 the pressure and measured the elastic force. As Mr. Boyle
ected to dry the air contained in the tube, his experiments,
which he pushed as far as a pressure equal to four atmospheres,
showed only a very near approximation to the law as stated above,
and which only applies to perfectly dry air.

About the same time, or shortly after, M. Mariottc.
brated Fronch physicist, arrived independently at the same re-
mit : .rdingly this law of the relation between the elastic
i and density of aii is culled indifferently P>«»\ •!«•'> «>r Mari<

It IKIS been mentioned that the results of Mr. Boyle's ex peri -
d nut 4 .iblish his law of pressures, but

inatic.n to it. As the subject is one of the

* A ( nt«, t Ilistoiro dc I1 Academic Royale dea

il, touching tli.' Spring Sciences, vol
Air.fcc. Ox
Trim-tact., vol. Hi. p. 845 (1668).

136 VAPORIZATION AND LIQUEFACTION. [BOOK I.

importance in physics, it has been, accordingly, fre-
quently submitted to the test of experiment, and the result hus
been a gradually increasing conviction of the accuracy of the law,
as applied to dry air, and at a constant temperature.

This conviction acquired additional strength from the experi-
ments made in 1830 by MM. Dulong and Arago, as members of
a Commission appointed by the Academy of Sciences in Paris,
to investigate the law of elastic forces of aqueous vapour at high
temperatures. In the course of those experiments it was neces-
sary to construct a manometer, an instrument which serves to
measure the elastic force of a gas or vapour by the amount of
compression which it produces in a given mass of air ; and in gra-
duating this manometer, which was done by means of a column
of mercury, as in Mr. Boyle's experiment, the Commissioners ar-
rived at the result, that his law is strictly true up to a pressure of
twenty-seven atmospheres, and probably to a considerably higher
limit.

For the purpose of ascertaining whether this law extends to
other permanent gases, M. Pouillet* has compared them with air in
this respect, by means of a very simple and ingenious apparatus,
which enabled him to extend his comparison as far as a pressure
of 100 atmospheres. The following are his results.

(i). As far as 100 atmospheres, oxygen, nitrogen, hydrogen,
nitric oxide, and carbonic oxide, follow the same law of compres-
sion as atmospheric air.

(2). Sulphurous gas, ammoniac gas, carbonic acid, and pro-
toxide of azote commence to be sensibly more compressible than
air, when they have been reduced to one-third or one-fourth of
their original volume; and there is little reason to doubt that this
difference exists for even smaller changes of volume.

(3). Protocarburetted hydrogen and bicarburetted hydrogen,
which do not liquefy at 8° or 10° C. under a pressure of 100 at-
mospheres, are yet sensibly more compressible than air.

As a proof of the variations which the compressibility under-
goes, M. Pouillet gives the following Table.

* Elements <le Physique, vol. i. p. 328.

CHAP. II.] VAPORIZATION AND LIQt I

'37

TABI.K of i "/y.WA ilify of the undermentioned Gase*, as re-

ferred to Air.

Pressures.

Theoretic

Yuli.

Carbonic
Add.

Protoxide of
Azote.

Protocarbu-
ratttd
Hydi

Bu-arbun-ttnl
Hydrogen.

i atmos.

I.OOO

i.

I.

I.

j

2

0.500

i.

0.996

0.998

0.994

4

0.250

i.

0.988

0.995

0.989

5

0.200

0.989

0.983

0.992

0986

6.67

O.I5O

0.980

0.971

0.989

0.983

10

O.I 00

0.965

0.956

0.981

0.972

I5-38

0.065

o-934

0.923

0.949

0.962

20

0.050

0.919

0.896

0.956

0955

25

0.040

0.880

0.849

0.951

0.948

33-3

0.030

0.808

0.787

0.951

0.931

40

0.025

o-739

0.732

0.940

0.919

50

0.020

....

0.907

0.899

83

0.

....

....

....

0.850

The numbers in the last four columns were obtained by di-
viding the volume of the gas, at the corresponding pressure, by
volume which air would have had at the same pressure. We
see that these quotients form a decreasing series in the case of

-. and that the law of decrease is tolerably regular.
Tho carbonic acid liquefied at 45 atmospheres, the tempera-
ture l>eing 10° C. ; protoxide of azote at 43 atmosphere.- and 1 1°.
The liquid appeared perli-etly transparent. At 10° anmumiaeal
gas liquefied under a pressure of 5 atmospheres. The liquid had
a greenish-yellow tint.

At 8° sulphurous gas liquefied under 2$ atmosphe
I all the cases of liquefaction whieh M. 1'ouillet observed,
und that it was always possible to augment e.m-iderahlv the
. without reducing the whole of the gfj to the liquid
; and -till he considered it as certain that u.-itli.

r, DOT anv of the m«>re permanent gases, was mixed with
I • d. in connexi..n with

that in consequence of some mvgulariii,- \\-hirli
Mr. ! <>n ..I' the va;

i

138 VAPORIZATION AND LIQUEFACTION. [BOOK I.

olefiant gas and protoxide of azote, and also in the pressure to
which the liquefaction of phosphurctted hydrogen appears due,
that distinguished chemist was led to suspect that those g;;
Avere either not perfectly pure, after all the care which was taken
in their preparation for his experiments, or that they are, in
reality, compound bodies, consisting of different substances so-
luble in each other.

More recently, M. Regnault has investigated directly the ac-
curacy of Boyle's law as applied to some of the permanent gases.
He has observed* that in all previous methods it was the same
mass of air or other gas which had been operated on, and which,
under constantly increasing pressures, was compressed into vo-
lumes constantly diminishing, until they became so small that
any deviation from the law in question was imperceptible. To
avoid the errors arising from this cause, M. Regnault operated on
different masses of gas at different pressures contained, in a glass
tube of about three metres in length, and from 8mm to iomm in-
ternal diameter. The gas, at the commencement of each experi-
ment, occupied q. p. the same volume F0 under different pressures
PO ; the pressure was then increased until it attained an amount
PI, which reduced the original volume about one-half. Tho
volumes F0, F,, and corresponding pressures P0, Pt, which were
produced, as in the former experiments, by columns of mercury
of different heights, were carefully ascertained, and on making all
necessary corrections, for an account of which the student is re-
ferred to the original memoir, M. Regnault arrived at the result
that Boyle's and Mariotte's law is not strictly true for any gas.

V P

He found that the ratio -^ -f- -rr1 , which, according to this law,

y\ "^

should always be equal to unity, is less for air, nitrogen, and car-
bonic acid, and greater for hydrogen, and that the difference

V P

— ? H- — - - i goes on increasing regularly with the pressure.

Thus when air occupying a volume equal to i , under a pres-
sure equivalent to 9336imn.4i of mercury, was compressed into u

* Meinoires de 1'Institut, tome xxi. p. 369 (1847).

CHAP. II.] VAPORIZATION AND LIQUEFACTION.

volume equal to 0.50009, its elastic force was represented by

V P

;im!".09, and consequently the ratio -p ~ — - equalled

M * 0

1.006366. M. Regnault remarks, that the elastic force of air.
under a pressure of about twenty-five atmospheres, is a little more
than one-seventh of an atmosphere less than it would be v.
le's law strictly true.

The deviation is considerably greater in the ease of carbonic
. Thus when this gas, under a pressure of 6820""". 22, was
compressed into a volume bearing the ratio i 13.5 to that origi-
nally occupied by it, its pressure was represented by 2O284mm.o8,

V P

and the ratio -4' -f- — 1 = 1.177293.

M •* 0

Hydrogen, it has been mentioned, also deviates from Boyle's
law, but in an opposite direction to air and the other gases exa-
mined. •' Wliile air and the other gases are more compressed than
ought to be, according to this law, hydrogen suffers a less
compresMon, and its compressibility diminishes as the pre>

la-tic force of hydrogen, then, is analogous to
that of a metallic spring which otters a resistance to compression,

g with the force applied."*

In confirmation of these results, ! uilt mentions the

that tin: value of the coefficients of expansion ofuir, nitiv

>nic acid, as determined by tin- <lir«-f method of dilatation
let than that derived from the in, 1 1 tod of elastic force*
(53), while the contrary is the case with hydrogen.

perature has a considerable influence on th.-e n-ults.
Thus M. IJe-jnault found that at i oc'J the coinpres.-ihilit y of air
much less from the ordinary law than at common tei;

Finally, M . Renault ifofopUUOD tliat ! .nid Mai

law may be considered a " limit law." wliieh n>|y

except \\hen gases are infinitely dihited. :md from which

\V- D oeed the |ih. ndin^ tin;

->73«

140 VAPORIZATION AND LIQUEFACTION. [BOOK I.

formation and liquefaction of that class of gases specifically .termed
vapours.

98. Vaporization by Ebullition. — The transition from the li-
quid state to that of vapour, termed in general vaporization, takes
place in two ways, which are respectively called ebullition and
evaporation. In the former the vapour is formed through the
whole of the liquid mass, in elastic bubbles, whence its name is
derived ; in the latter it is emitted merely from its surface. The
former takes place at a certain temperature, determined by cir-
cumstances to which we will presently refer ; the latter, in most
liquids, at all temperatures. We will first consider the process
of vaporization by ebullition.

If we heat water contained in an open vessel, and in free air, we
see that, after it has attained a certain temperature, bubbles of va-
pour form on the bottom and sides of the vessel, are subsequently
detached from them, and rise through the liquid mass until they
reach the surface, where they mix with the surrounding medium.
The temperature at which water thus enters into a state of
ebullition depends (i.) on the pressure to which it is submitted ;
(n.) on the presence or absence of foreign bodies, whether (i) in
solution, or (2) in contact. We will treat of these several con-
ditions separately.

99. i. Influence of Pressure on Temperature of Ebullition. — It
has been observed that at the tops of high mountains, and on other
elevated situations, where the atmospheric pressure is considerably
diminished, water boils at temperatures continually decreasing as
the altitude increases. Thus at Quito, standing at an elevation
of about 9540 feet, where the barometer has a mean height of
20.7 inches, water boils at 90°. i C., or I94°.i8 F. At the Hos-
pice of St. Gothard, at a height of 6800 feet, and under a mean
pressure of 23 inches, the boiling point is 92°. 9 C., or 199°. 22 F.
Water boiling in free air, then, is not equally hot at all places on
the earth's surface, and hence is not everywhere equally effective
for the cooking of food, and other domestic purposes.

The effect of diminished pressure in reducing the boiling point
of water is exhibited in a very simple and striking manner by boil-
ing a small quantity of this fluid in a Florence flask over a spirit

CHAP. II.] VAPORIZATION AND LIQUEFACTION. 141

lamp, li, when all the air lias been expelled from the upper part of
the llask, and replaced by steam, we olooe its aperture tightly with
a cork, anil remove it iroin the lamp, the ebullition is renewed,
and is rendered still more violent by pouring some water on the
>{' the ilask, which produces a partial condensation of the
,1 within, and a consequent diminution of its pressure. And
the water may by this means be kept in a state of ebullition at
temperatures considerably below 100 C. The same effect is pro-
dueed by placing water which has just ceased boiling under the
receiver of an air-pump, and gradually diminishing the pressure
fii it.- suri

The relation between the pressure and the boiling point is,
however, more accurately exhibited by means of the following
apparatus. In a retort, A (fig. 60), a quantity of water is heated,
whose temperature is indicated by the thermometer, t\ attached
to the neek of this retort is the tube, TT', whose other end opens
into the globe, B, which is connected with an air-pump by means
of the tube, tt, furnished with a stop-cock, r. This globe is also
connected with a mercurial gauge, for the purpose of determin-
ing the pressure within it. Round the tube, TT', is a cylinder
lining cold water, which ilows in a constant stream through
the pipe, K, into a rec . Sect of this current is con-

tinually to condense the vapour ri.-'mg from A, and thus prevent
.-minting and increiiMng the pressure on the surface of the
I manner of operating with this apparatu- i> iir.-t to
;.Tiniiied pre.-.-ure in n, and then to rai.-e the tempe-
rature of tin: retort until the water enters into a state ofrlmlli-
. when its boiling point, OOCmpoadllig to this pn

..•rmoiii. «ter {.

When vapour forms in the l.ody of a liquid mass, it is plain
that it.- ela.-tie f'-ree is equal to the piv.-Miiv i.n the surface of the
liquid, i: hy the pressure of the stratum of liquid •

point wl.- formed, According «a the bubble

irfaee tliis proMire diminishes and ultimately

1 medium, and hence the

Me purpose of detei-

min. Jtced from water at dille-

142 VAl'OKI/.ATION AND LIQUEFACTION. [BOOK I.

rent temperatures. We will return to this subject in the last
section of this chapter, where we will also notice the application
which has been made of the connexion between the boiling point
of water and its pressure to the measurement of mountains.

As the boiling point of water depends on the pressure to
which it is exposed, it follows that in deep vessels, when the
whole of the liquid which they contain is in a state of ebullition,
the lower strata of water must have a higher temperature than
those nearer the surface. It follows, also, that if we increase by
any means the pressure on the surface of water, its boiling point
will be at the same time raised, and thus its temperature, which
in free air can never much exceed 100° C., may be raised to a
considerably higher limit. This effect may be produced by heat-
ing it in a strong steam-tight vessel, of moderate dimensions, as
the constantly accumulating vapour collected in the upper part
of such a vessel will exert a rapidly increasing pressure upon the
surface of the water, and thus, as we have seen, retard its ebul-
lition.

A vessel constructed on this principle, and called Papin's di-
gester, is sometimes used for raising water to temperatures above
the ordinary boiling point. It was invented by the person whose
name it bears, a distinguished physicist of the seventeenth cen-
tury, and is simply a strong metallic boiler, with a steam-tight
lid, and furnished with a safety valve, which may be loaded to
any required pressure short of that which would risk the rup-
ture of the vessel. Such an apparatus is necessary for ordinary
culinary operations at high levels, where, as we have mentioned,
the temperature at which water boils in free air is insufficient
for such purposes, and is besides useful for exhibiting generally
the solvent power of water at high temperatures.

If water is boiled in a vessel furnished merely with a small
aperture for the escape of the steam, the pressure, and conse-
quently the boiling point, will depend on the area of this aper-
ture as compared with the quantity of steam generated in a given
time, which, as experience shows, varies as the area of the heat-
ing surface. M. Pouillet gives the following table of the approxi-
mate value of the boiling point in connexion with this ratio.

(HAP. II.] VAPORIZATION AND LIQUEFACTION. 143

1. mperature of Water in r>..il.-r.

Ratio of Orifice to Heating Surface,

100° C.
I05

"5

I38

i — 1000 and upwards,
r — 5000

I — 1 0000
I — 2OOOO

TOO. Phenomena presented by Liquids raised to very high Tein-
I hinted Space. — On continuing to raise the tempe-
rature of a liquid contained in a closed space oflimited capacity,
the density oi' the vapour which is formed, and consequently it-
elastic force, increases very rapidly, and retards, as we have re-
marked, the point at which it enters into a state of ebullition.
In the case of some liquids enclosed in a space but little larger
than their own volume, M. le Baron Cagniard de la Tour* ob-

d that, on being raised to a certain temperature, they passed
instantaneously and totally into the state of vapour. The appa-
ratus he made use of consisted of a short siphon of strong glass

. both ends of which were closed, and the curved part filled
-with mercury; above the mercury in one arm was contained the
liquid un which he operated, uml in the other atmospheric air,
whose compression served to measure the elastic force of the Mi-
pour furnished by the liquid. The temperature (.{'the liquid
was raised either by a bath of fixed oil or a blow-pipe. By

MS of this, apparatus M. Cagniard de la Tour observed, that at

nperature of 150° C. ether passed completely into the state of

>ur, occupying a space somewhat less than twice the original
v.'luim- nfthe liquid, and having a pivssure nl'thirt y-sev.-u at :
pin-res; Hinilarly. at a K-mprratun- of 207°, alcohol und.-r\\ nit the
•tir, OCCUj' - than three times the

nal volume of the liquid, hud an elastic t il tu IK;

-pheres. Sulphun-t uf carbon also at 220° passed int.

..t' vapour, having a force equal to seventy-right utmu.<j>h,

: in producing the same result in the case of nrtilied
essence of petroleum, but laded in that «•! \' the

•- il>' ( 'liiini'1 <t '!• I'liysique, tonn ."*, 178 (1821) ; xxii. p. 410;

23).

I_j_j. VAPORIZATION AND LIQUEFACTION. [BOOK I.

temperatures necessary for the experiment, this latter liquid ac-
quired so powerful a solvent property as to attack the alkali of
the glass, which communicated to it a tint of greenish hue, that
deepened as the temperature increased, until on one occasion it
became nearly black. On being cooled again the water reco-
vered its original transparency. In all the cases in which the heat
was pushed sufficiently far, the tubes exploded before the water
was completely reduced to vapour, partly owing, no doubt, to
the disintegration of the glass, as well as to the enormous elastic
force of the aqueous vapour. The experiment is, in all cases,
one of considerable risk, and requires to be conducted with all
the precautions which are adopted where similar danger is ap-
prehended.

Connecting this phenomenon with the liquefaction of gases,
Mr. Faraday* makes the following ingenious observations :

" M. Cagniard de la Tour has shown that at a certain tempe-
rature a liquid, under sufficient pressure, becomes clear, transpa-
rent vapour or gas, having the same bulk as the liquid. At this
temperature, or one a little higher, it is not likely that any in-
crease of pressure, except, perhaps, one exceedingly great, would
convert the gas into a liquid. Now the temperature of 166°
below o°, low as it is, is probably above this point of temperature
for hydrogen, and perhaps for nitrogen and oxygen; and then no
compression, without the conjoint application of a degree of cold
below that we have as yet obtained, can be expected to take from
them their gaseous state. Further, as ether assumes this state
before the pressure of its vapour has acquired thirty-eight atmos-
pheres, it is more than probable that gases which can resist the
pressure of from twenty-seven to fifty atmospheres, at a tempera-
ture of 1 66° below o°, could never appear as liquids, or be made
to lose their gaseous state, at common temperatures. They may,
probably, be brought into the state of very condensed gases, but
not liquefied."

101. n. Influence of foreign Bodies, whether in Solution or in
Contact, on the Temperature of Ebullition; Theory of M. Magnus.—
This subject has been examined with particular care by M. Mag-

* Philosophical Transactions, 1845, p. 171.

CHAP. II.] VAPORIZATION AND LIQUEFACTION. 145

• an<l M. Donny,f ail(l we purpose to lay before the student
the views of those writers on the process of ebullition in this and
the following paragraph.

M . .Magnus, in the course of his experiments on the elastic force
of vapours, remarked, what had been observed by previous phy-
sicists, that water which has been well boiled does not generally
pass into the form of steam in glass vessels until it has acquired a
temperature considerably above that due to the force of its vapour,
and that the formation of steam then takes place suddenly and
with great violence. From this it follows, that the force re-

ite for the disengagement of the steam is greater than its
expansive force subsequently, and the difference of these forces
M. Magnus refers to the attraction of cohesion existing between
the particles of the liquid, which requires to be overcome at the
moment of formation of the steam, in addition to those pressures
which the vapour itself subsequently sustains.

Hence he concluded, that whatever would tend to affect the
cohesive force of those particles, either generally throughout the
mass, or at certain points, would affect the temperature of ebulli-
tion.

(i.) On this principle, he remarks, we can understand why
salts in solution raise the boiling point of water. For the cohe-
sion between water and salt being stronger than that between tin*
particles of water among one another, a stronger force, and conse-
quently a higher temperature, is requisite to overcome the cohe-
sion in the case of solutions than of pure water. Moreover, the

• •nee of a salt lowers the elastic force of vapour in contact
with water, as is proved by introducing a salt — for instance, chlo-
ride of sodium — into the water < -.miaim •<! in the vacuum of abaro-

•T, when the exp. rce of the vapour is immediately

diminished. And therefore the temperature of a saline solu

It be higher than that of pure water, to maintain vap»ur
of equal elastic foi

i also understand how the presence of bodies held
suspended in a liquid, or the snles of the containing vessel, if i

* PoggendorfTs Annaln. f Ann. do ('him. •>( d«- Phy*., tome art

1846).
U

146 VAPORIZATION AND LIQUEFACTION. [BOOK I.

have a less attraction for the particles of the fluid than the latter
have for one another, will loiver the boiling point. And this will
always be the case if physical contact does not exist between
such bodies and the liquid, that is, if they are not completely
moistened by it. Accordingly, sawdust or insoluble powders,
diffused through the fluid mass, and the sides of a metallic ves-
sel, which, as is well known, are never completely moistened at
all points by water, lower the temperature of ebullition to that of
the vapour. But if the water is boiled in a glass vessel, espe-
cially if the sides of the latter are perfectly cleaned by heating sul-
phuric acid in it up to 150° C., and then rinsing it with distilled
water, by which means the contact is rendered more perfect, and
the cohesive force of the glass on the particles of water stronger,
the boiling point will rise to 105° or 106°. Now, as M. Mag-
nus remarks, the action of the sides of the vessel, and of solid
bodies in general, may diminish but cannot raise the temperature
of ebullition ; for if the force of attraction of such bodies for the
fluid molecules were stronger than that of the latter for one ano-
ther, the only effect would be that the ebullition would commence
at the centre of the liquid, and not at the sides. Accordingly,
no liquid can assume a higher temperature than that at which
the expansive force of the vapour suffices to overcome the pressure
and cohesion of the liquid. And the highest temperature of ebul-
lition observed in the case of a pure liquid under a given pressure,
is its true boiling point at that pressure, and is the same as that
which it would indicate if it could be boiled in vessels formed, as
it were, of the same liquid, or in vessels the sides of which would
retain it everywhere with the same force as its particles attract
one another.

The true boiling point of water, therefore, according to M.
Magnus, is about 105° C. ; and as its vapours at 100° have an
elastic force equal to the atmospheric pressure, it follows that the
difference between this force and that due to vapours at 105°,
or about one-fifth of an atmosphere, is the measure of the cohe-
sive attraction of the particles of water.

1 02. Theory of M. Donny. — Such are the views of M. Magnus
on this subject, and the facts from which he derives them. M.
Donny, however, has been led, by his investigation into the

CHAP. II.] VAPORIZATION AND LIQUEFACTION. 147

force of cohesion of liquids, to conclude that the boiling point of
water, as defined above, that is, the temperature at which water,
perlectly free from all foreign bodies, would pass into the stat«-
of vapour throughout its mass, is considerably higher than even
the highest limit assigned by M. Magnus. Having observed
that a column of sulphuric acid, well freed from air, of im.255 in
height, remained suspended in the closed branch of a manometer,
which he had adapted to an improved air-pump of his own con-
struction, when the pressure on the surface in the open arm did
not exceed that due to 5mm of the acid, M. Donny was led to the
conclusion that the cohesion of the particles of liquids to one ano-
ther, and to solid bodies, must be much greater than had been
previously suspected ; and that the apparent feebleness of this
power, when measured by direct experiments, was owing to the
me mobility of the particles of fluids and the presence of
gaseous bodies diffused through their mass. He was accordingly
led to examine the boiling point of water when deprived, as far

ossible, of air; and found that, when enclosed in a tube of
iar form, and subjected, through the whole of the expcri-
a very feeble pressure on its surface, it might be raised
to temperatures of 113°, 121°, 128°, and 131° C., without enter-
ing intu a state of ebullition. At last, on plunging it in a bath

•Moride of calcium, which rose, in about two minutes and
a half, from 132° to 138°, when the portion of the water sub-
mitted to the action of the hrat had acquired a temperature of
about 135°, it was instantaneously converted into vapour, and
projected with considerable force the remainder of the column
into the balls terminating the tub- ' khil M . U-miycon-

elu«; ic mutual force of cohesion of the particles •>(' water

is equal to a pressure of about three atmosph' 1 in this

strong cohesive force finds ;m explanation of the phanomenoB
called " soubresaut," orjumpi -metimes observed in

liquids when in a state of ebullition, a.- well as, probably, of those
hirh occur s< ntly in steam boilers, and

let to perplex engineer- :md physicists. 1
says M. Donny, M by the eil'.-et of boiling, liquids lose th-

p. nt <»f the air which they hold in solution, consequently the

in a sensible

148 VAPORIZATION AND LIQUEFACTION. [BOOK I.

manner, and permits the liquid to attain a temperature conside-
rably above its normal boiling point ; this elevation of tempera-
ture determines the appearance of new bubbles of air, the liquid
then separates abruptly with a " soubresaut," a large quantity of
vapour forms, and consequently a reduction of temperature ensues,
which restores a momentary calm to the liquid. Presently the
same causes reproduce the same effects, and the phenomenon is
renewed with increased violence ;" and, as M. Donny shows, may
eventually result in a violent explosion, when occurring under
circumstances analogous to those of a steam boiler.*

From these facts, proving the strong cohesive attraction of
liquid particles, joined to the well-known tendency of all fluids to
assume the vaporous state at all temperatures, M. Donny con-
cludes that the superficial stratum of liquids possesses a peculiar
property in this respect, and has hence been led to form the
following theory of ebullition. " The elevation of temperature
of a liquid produces the formation of small bubbles of air in the
hottest portions of its mass, and consequently on the side of the
containing vessel nearest the source of heat ; each of these bubbles
presents to the liquid molecules which surround it a surface which
facilitates the vaporization of those molecules; and when the ten-
sion of the vapour becomes sufficient to counterbalance the pres-
sure to which those bubbles are exposed, there is no further
resistance to the development of the vapour, which then forms
currents that traverse the liquid, and produce the phenomenon of
ebullition.

" I think, then," continues M. Donny, " we are justified in
concluding that ebullition is nothing but a kind of rapid evapora-
tion, which takes place at those internal surfaces of a liquid that
bound the bubbles of aeriform fluid which are formed through
its mass."

We will conclude these remarks on the phenomenon of ebul-
lition with the observation of M. Magnus, that " there does not
exist an older physical experiment, nor one more frequently re-

* These " soubresauts," which are more phuric acid, may to a considerable extent
violent in the case of fluids boiled in glass be prevented by throwing scraps of metal,
N, and especially in the case of sul- platina, &c., into the boiling liquid.

CHAP. II.] VAPORIZATION. AND LIQUEFACTION. 149

peated, than that of boiling water; but nevertheless what occurs
in the process was not sufficiently known, and even now much
still remains unexplained.''

103. Vaporization by Evaporation. — If a small quantity of
water or other liquid, volatile at ordinary temperatures, is placed in
a shallow vessel in free air, it is found to pass gradually into the
state of vapour, and disappear completely after a space of time
depending on the quantity of liquid, on the extent of surface
exposed to the air, on the amount of vapour of the same li-
quid existing in the surrounding medium, and on the common
temperature. If the liquid is in vacuo, and the vapour is removed
us fast as it is produced, the result is the same, but the rate of
evaporation is infinitely more rapid.

The connexion between these several conditions will be better
understood after we have investigated the laws of the elastic force
and density of vapours in relation to their temperature, which
we purpose to do in the following section.

104. If eat absorbed in the Formation of Vapour. — We have
observed that in the transition from the solid to the fluid state

is an absorption of a considerable quantity of heat,

forming the constituent or latent heat of the fluid; and a similar

phenomenon manifests itself, in a still more striking manner,

in the passage from the fluid to the vaporous state. It' this

is effected by the way of ebullition, the latent heat of

vapour is supplied by the fire or other source of heat pn-

hullition, all the heat from which is expended in

the formation of vapour, and the temperature of the boiling

liquid consequently remains unaltered. Hut if the vapori/.a-

is Hl'.vted by evaporation, the heat i for the for-

>n of the vapour is taken from the liquid itself ami iV.au

unding bodies; and if the rate of evaporat i \ rapid,

.;•_' to the extent of surface, and the previous absent

pour in the Mirroundin^ medium, and if. at the same time, the

amount <>i he.it radiated from nei;.dih«,nrmir b«'d py small,

liquid is rapidly and c.msiderahlv lowered.

Thu- in clear Mimmer i ;ik;l-

bly i . aqueous vapours, and the absence of clouds prevent-

n by ivfl«-xi«'u of lV«»m the earth, v,

1^0 VAPORIZATION AND LIQUEFACTION. [BOOK I.

in shallow vessels is frequently frozen. And in the same way if
water is placed under the exhausted receiver of an air-pump, in
a shallow vessel, over a dish of strong sulphuric acid, which
absorbs and condenses the aqueous vapours as fast as they are
formed, the same result is obtained.

We will return to this subject in the second chapter of Book

II.

105. Leidenfrost's Phenomenon. — Before proceeding to the

investigation of the laws of vapours, we must notice a singular
phenomenon connected with the vaporization of liquids projected
on the surface of solid bodies raised to a very high temperature.
Although this phenomenon must have been frequently noticed
previously, yet it was examined scientifically for the first time by
Leidenfrost, who published his observations in 1756, in a thesis
entitled " De Aquae communis nonnullis Qualitatibus," and is
hence generally called Leidenfrost's phenomenon. It is this. If
a drop of water or other liquid is thrown upon a surface raised to
a very high temperature, the liquid does not moisten or diffuse it-
self over the surface, but forms a flattened ellipsoidal mass, which,
if the drop is sufficiently small, assumes the spheroidal form, re-
volves rapidly round a shifting axis, and, the heat of the surface
being kept up, evaporates with extraordinary slowness, without
ever entering into a state of ebullition.

This phenomenon, which appears so completely opposed to
all the known facts of the communication of heat, as to merit the
appellation of the caloric paradox, has been examined by several
physicists.* We will briefly mention the principal facts con-
nected with it, as elicited by their researches.

There are two peculiarities connected with this phenomenon ;
the first is the fact that the liquid does not moisten the hot sur-
face, but assumes, when in sufficiently small masses, the spheroidal
form ; the second is, the absence of equality of temperature be-

* De Saussure, Journeys in the Alps, (1832), No. 8; Baudrimont, Ann. dc

vol. iii. ; Klaproth, Annales de Chimie et Cftim. ct de Phys., tome Ixi. p. 319

de Physique, tome xxxv. p. 325 (1827); (1836) ; Laurent, Ibid., tome Ixii. p. 327

Fischer, Poggendorff's Annalen (1830), (1836); Boutigny, Ibid., tome ix. p. 350

No. 8 ; Lechevalier, Journal de Pharmacie, (1843), tome xi. p. 1 6 (1844); Boutan,

tome xvi. ; Buff, Poggendorffs Annuhn Mem. Acad. de Rouen (1848), p. 48.

CHAP. II. J VAPORIZATION AND LIQUEFACTION. 1 5 I

tween the liquid drop and the hot plate. Buff appears to have
been the first to point out the connexion between these two con-
ditions. He observes that if a clean silver spoonful of water is
placed over a lamp, it may be held without inconvenience while
the water is boiling, until the last drop is vaporized, the heat
communicated to the metal being in this case transferred to the
fluid, and absorbed in the latent state by its vapour. But if the
inside of the spoon is covered with a coating of lampblack, which
does not admit of being moistened by water, the spoon, in this
. becomes intolerably hot before the water boils. Nor is this
owing to the non-conducting nature of the lampblack, for if ano-
ther carbonaceous coating, which admits of being moistened by
r, is substituted for it, this effect is not produced. It follows,
therefore, that the non-moistening of the surface, and consequent
assumption of the spheroidal form by small masses, is intimately
connected with the non-establishment of thermic equilibrium.
\V will notice the facts connected with these two conditions se-
parately.

1 06. I. Assumption of spheroidal Form by small Masses of Li-

jected on hot Surfaces.

(i.) M. Boutigny is of opinion that all liquids are capable of
assuming this .-tate, and thinks it probable that the volumes of
i spheroids are inversely proportional to their specific gravi-
ties, so that the masses of different liquids capable of assuming
this state are equal. He ascertained also that the velocity with
•h the liquid is projected does not affect the result, for, on
vint/a quantitv of distilled water from the cupola of tin1 Pan-
theon of Paris on a platina di-h. seven inches in diameter, main-
a red heat, <»n the floor of the building, the total height

•t. the water in falling broke up into drops of dill'
ich consequently reached the ground with very dillerent
-, hut all which struck the platina vessel parsed imme-
diately into tin- spheroidal sta

The -am<- physicist ascertained that the lowest tempera-
irface capable of producim: this state varie- with the
;ility of the liquid, and is higher the higher the boiling j

of the lat:< I tampon

of the plate to be 171° I ohol 134°, and for ether 61°.

I £2 VAPORIZATION AND LIQUEFACTION. [BOOK I.

M M luuul* has shown that it also varies with the tempera-
.•1'tho projected liquid and the nature of the surface. Thus

\vater at 100° C. the requisite temperature of platina is 120°,
and of glass 1 80° ; for water at o° those temperatures are 400°
and 800° respectively.

(iii.) The spheroid apparently does not touch the plate. If
the surface is plane, the eye placed on a level with it can see
the light of a taper between the drop and the plate. Moreover,
M. Boutigny has shown that a drop of nitric acid in the spheroidal
state has no action on a silver or copper surface, nor has one of
dilute sulphuric acid any action on iron or zinc, while if a cold
wire of those metals is introduced into the drop it is immediately
and powerfully attacked. Further, the same writer mentions,
that if a large drop of water, sufficient to form, a very flattened
ellipsoid, is projected on a silver capsule nearly plane, and if an
iron cylinder of about .4 inch diameter is raised to a white heat,
and introduced into the drop, the latter assumes a form which,
" a tort on a raison," he compares to Saturn's ring.

(iv.) If sand, iron filings, pounded glass, &c., are mixed with
the fluid forming the drop, they do not sink to the plate, as
might have been expected from their greater specific gravity, but
are held suspended by the spheroid, and according as the fluid
evaporates these particles approach more and more, until they
are finally deposited on the surface in the form of a hemisphere
or a cup, or a disk pierced or not with a central aperture.

(v.) The most probable explanation of the non-moistening of
the surface appears to be, that it results from a change in the di-
rection of the resultant of the capillary forces, owing to the in-
creased distance of the molecules of the solid body from one
another, in consequence of the action of heat. Some physi-
cists are of opinion that the detachment of the drop from the
plate may be accounted for by supposing it to rest on a cushion
of its own vapour ; this, however, appears extremely improbable,
in consequence of the low density of the latter. It appears more
probable that the drop is in a state of perpetual and rapid oscilla-
tion to and from the surface ; and M. Boutan suggests that this

' Berzeliu?, Rapport (1843), p. 17.

CHAP. II.] VAPORIZATION AND LIQUEFACTION. I 5;

vibratory movement may be owing to the expansion and contrac-
tion of solids arising from change of temperature not taking place
uniformly, but by a rapid succession of intermittent motions, and
that the musical tones produced in the experiment noticed by
Mr. Trevelyan result from the same cause.

107. II. Non-Establishment of thei*mic Equilibrium in spheroidal

(i.) In order to ascertain the temperature of the liquid in the
spheroidal state, M. Boutigny made use of a very small thermo-
meter, the bulb of which he immersed in the drop. He thus ar-
1 at the result ** that bodies in the spheroidal state remain
constantly at a temperature inferior to that of ebullition, what-
ever may be the temperature of the vessel which contains them."
This temperature he determined to be, for water, 96°.$ C. ; for
alcohol, 75°. 5 ; for ether, 34°. 25 ; for chloride of ethyle, io°.5 ; and
for sulphurous acid, - io°-5.

M. Boutigny 's method of determining these temperatures is
liable to serious objections, and does not appear capable of giving
accurate results. It can only be relied on as giving a limit which
the temperature of the drop cannot exceed.

The method adopted by M. Boutan appears susceptible of
much greater accuracy. It depends upon the principle that if a
bar of any metal is placed in metallic contact at its two extivmi-
•vith bars of a different metal, and if the points of contact are
itained at different temperatures, an electric current is pro-
duced in tin- metals wlu-n loiminLT part of a closed eireuit, tin*
.isity of which varies with the difference hetw.-en tl,

id is capable of l>einLr rendered sensible by its at;
on a magnetic needle. The apparatus employed by M. Boutan
isted of a very fine platina win-, attached at i:

of iron win- equally line. The attachment was effected
by raising tl.< ratnre of the in.n to the point at which it

united with tin- platina, without auv inter -Ider. The

•Imient svas not above i"1"1 in length. Tin-

1 as follows. The free , the

screws of a

pal\ : he kin-: • d hv M.

X

154 VAPORIZATION AND LIQUEFACTION. [BOOK I.

placed, one in the liquid spheroid, the other in a quantity of
mercury in which was plunged the bull) of a very sensitive mer-
curial thermometer. Any difference of temperature between the
spheroid and mercury was exhibited by the deflection of the gal-
vanometer needle ; and by raising or lowering the temperature of
the mercury until the needle resumed its normal position, the two
temperatures might be brought to a state of perfect equality, and
thus the temperature of the drop ascertained with a great degree
of accuracy.

M. Boutan gives the following general account of the results
of his experiments :

" I have ascertained that the supposition of the liquid in the
spheroidal state having a constant temperature throughout its
mass is erroneous. When the mass is at all considerable, the
different layers of the liquid have different temperatures. It is
only when the drops are small, and the vessel has attained a sta-
tionary temperature, that the calorific equilibrium is thus esta-
blished in the drop. I have also succeeded in ascertaining the
influence exerted by the presence of a solid body plunged in the
liquid mass, and which is at the same time in contact with the
heated surface. The temperature of the liquid immediately rises,
but still remains below its boiling point, although the body im-
mersed may contain within a cavity in it the same liquid in a state
of ebullition. Only, bubbles of vapour form on the surface of me-
tallic bodies introduced into the drop, to which they adhere firmly,
and from which they are detached in small numbers. Finally,
I have, by the aid of the same instrument, succeeded in making
a considerable number of numerical determinations, which I have
not yet been able to complete, and which I shall shortly have
the honour of communicating to the Academy. These numbers
appear to me to furnish the first elements necessary to connect the
theory of calefaction with the well-established laws of caloric."*

(ii.) With respect to the temperature of the vapour, M. Bou-
tigny is of opinion that it is the same with that of the enclosing
vessel, as, indeed, is probable, without evidence to the contrary.

(iii.) The experiments made with anhydrous sulphurous acid

* Mem. Acad. de Rouen, p. 50.

CHAP. II.] VAPORIZATION AND LIQUEFACTION. 155

-o extraordinary as to deserve special notice. M. Boutigny

having raised a platina capsule to a white heat, poured on it some

ames of anhydrous sulphurous acid. Watching the neck of

1 containing it, the acid was observed to be there in a

of ebullition, which ceased when it fell upon the capsule,

and assumed the spheroidal form. Its rate of evaporation was

incredibly slow, and it presented no signs whatever of ebullition.

(This liquid, it is to be observed, boils at about 10°). On pouring

distilled water, drop by drop, into the sulphurous acid while

in tliis state, it was instantly congealed, even while the capsule

remained at a white heat. And finally, on introducing for about

hall' a minute the ball of a small mattrass containing one gramme,

about fifteen grains, of distilled water, into the sulphurous acid in

spheroidal state, and then removing it, it was found, on being

broken, to contain a small fragment of ice.

On obtaining these results, says M. Boutigny, " J'eprouvai
• ur-la. une de ces jouissances de laboratoire qui ne sont con-

nues que des physiciens et de chimistes "

congelation of the water under those circumstances is
v explained. Its vapour is absorbed by the anhydrous acid
as quickly as it is formed, and the rate of evaporation is conse-
quently so rapid as to cool the temperature of the water, and
finally conceal it in the manner explained in (104).

iday also mention?,* in a letter to M. Bmitiirnv. that

In: i; 1 into a platina capsule, maintained at a red heat,

some ; id solid carbonic acid, and into the spin-mid liu-med

by these substances plunged a small metallic capsule containing

,t thirty-one grammes of mercury, which was si.lidilicd in

-econds.

!)•• Saussure was of opinion that there is a maximum
slowness of evaporation OORetponding to a cert ain t< •mperatui
.••! surface. Klaproth, who ma<le his experiment with \\
in ;m //••»« spoon, arrived at the conclusion that tli<

hi«jh'-r the tern;
MIT with a /•/•/////!/ capsule, ha-
at ti that th.

156 VALORIZATION AND LIQUEFACTION. [BOOK I.

poration increases with the temperature of the surface. The pa-
radoxical conclusion arrived at by M. Klaproth probably resulted
from the rapid oxidation, during the experiment, of the iron
1 which he employed. The time requisite for the evapora-
tion of o.i gramme of water in the spheroidal state, according to
M. Boutigny, when the surface is heated to 200° C., is fifty
times more than that required to produce the same effect by
boiling.

The slowness of evaporation of liquids in the spheroidal state
is most striking in the case of those which are most volatile, such
as sulphurous and carbonic acids, which, evaporating with ex-
traordinary rapidity under ordinary circumstances, appear com-
paratively fixed in the spheroidal state. The rate of evaporation
varies, within certain limits, with the form of the capsule, its po-
lish, its capacity, and its thickness.

(v.) Assuming the temperature assigned by M. Boutigny to
water in the spheroidal state to be even approximately correct,
it follows, from the preceding remarks on the rate of evaporation,
that the density of the vapour given off by it is far inferior to that
due to its temperature, and that accordingly there is neither equi-
librium of temperature between the surface and the liquid, nor
equilibrium of tension between the liquid and its vapour.

(vi.) We have seen (102) that M. Donny suggests that the ex-
plosive ebullition of water, when freed from air by long boiling,
may be one cause of steam-boiler explosions. M. Boutigny con-
ceives that the assumption of the spheroidal state by large masses
of water in those boilers may also produce the same effect. " When
the steam passages are closed," says this writer, " the temperature of

the boiler must rise ; the water is then exposed to the action

of two forces which neutralize each other, soil, the pressure exer-
cised by the vapour on the surface of the water, and the repul-
sive force of the boiler acting underneath. If a valve is now
opened, the steam rushes out with considerable velocity, a partial
vacuum is formed, and the water, repelled by the hot metal below,
and attracted, so to speak, by the vacuum, is driven to the upper
part of the boiler, and, falling back immediately in obedience to
the laws of gravity, assumes the spheroidal state. It then fur-
nishes but little vapour, thermic equilibrium no longer exists, and

CHAP. II.] VAI'OKIXATION AND LIQUEFACTION. 157

xplosion is imminent. This may be hastened by two cm
lirst, by the addition of a certain quantity of cold water; secondly,

lie lowering of the fires. The water in boilers may also pass
into the spheroidal state in consequence of a deficiency in the
supply, either from the negligence of the engineers, or defect
in the feed-pumps, &C."*

(vii.) It remains only to mention some of the explanations given
of the non-establishment of thermic equilibrium between a liquid
in the spheroidal state and the containing vessel. The first is,
that the heat in this case traverses the liquid without being ab-
sorbed by it. This, at first sight, appears probable, as we know
that liquids and other bodies are capable of being permeated by
radiant heat, as diaphanous bodies are by light. However, some
of the facts mentioned above show that this principle does not
apply to the present case, since the presence of particles capable

;e.-ting and absorbing the rays of heat, such as charcoal, sand,

iails to raise the temperature of the spheroid. Such a view
is also inconsistent with the formation of ice in the drop of sul-
phurous acid, us described in page 155.

second hypothesis advanced to account for this pheno-
menon is, that the rays of heat do not enter the spheroid at all.
but are reflected from its surface, and although there is no verv
ious reason assignable why this should l>e the case, yet it ap-

-, on the whole, the most probable explanati' I hi-

therto. It is due to M. Boutigny, who mentions, in confirmation
.is view, that if ft drop of nitric acid in the spheroidal -

to describe a curve on a silver capsule, the points of the

1 under tin' spheroid will appear of a brighter red than tin-
iest of the vessel, if the expei iinent i- pei formed in a dark room,
and if the <-oui>e of the liquid is afterward.- examined with atten-
. it will be found mammellated. cxhil/n | of incipient

n. '• This remark proves sufficiently," observes our author,
ki thai in the spheroidal Itftt

, tome xi. have used the express!* / ,t,.t,

a* ««niiv.ilrn( t<> tjiftntcr in t/it sfili, i <>t<l,il

t H-i 368. I hi* remark U rendered mifnuij

ll tobeobscrv«l tli

|.h. -11111111 n

!j8 LAWS OF VAPOURS. [BOOK I.

\Y • will conclude these remarks by observing, that some
.-h writers have called this phenomenon the calef action of ii-
iid say that a liquid is calefied when it exists in the sphe-
roidal form.

SECT. III. — LAWS OF VAPOURS.

1 08. General Properties of Vapours. A. In vacuo. — The laws
of the formation of vapours, and of the relations existing between
their elastic force and temperature, were first successfully inves-
tigated, about the commencement of the present century, by Mr.
Dalton. The results of his experiments were laid before the Li-
terary and Philosophical Society of Manchester in the year 1801,
and appeared in a volume of their Memoirs published in the fol-
lowing year. The apparatus employed by Mr. Dalton in his in-
vestigations of the general properties of vapours, was constructed
as follows.

ab (Fig. 48) represents a long barometer tube, inverted in a
tall cylindrical vessel full of mercury. The height of the mercurial
column in the tube is measured by a graduated rule, r, whose
point is brought to coincide with the surface of the mercury in
the reservoir. Preparatory to experiment, the inside of the tube
is moistened with the liquid whose vapour it is intended to ob-
serve, and the tube being filled with mercury lately boiled is in-
verted into the reservoir. The fluid moistening the sides of the
tube, being lighter than the mercury, rises to the top, where it
forms a thin film on its upper surface. The mercury is then
found to be depressed below the level at which it would stand
with a vacuum above it, by a quantity measuring the elastic force

described in the preceding pages 33 consti- His principal reason for this strange hy-
tuting a fourth state, in addition to the pothesis is, that metals, on cooling, take
solid, liquid, and gaseous. M. Boutigny the form of the vessel they occupy more ac-
.IU'U'-.-N that we only know metals in curately than in the liquid state; that
the solid, spheroidal, and gaseous states, they diffuse themselves over it, moist.cn it,
and that they pass immediate?!/ from the as it were, or metallize it rather ; and be-
first to the second of these, as ice as- sides that their U-mpwatnn- rises on soli-
.-niiir> tin- >|.lu-roidal form instantaneously dification.
when dropi^'il on a >urla«-i- sulliricntly hot.

CHAP. II.] LAWS 01 VAPOURS. 159

of the vapour emitted from the fluid. The space occupied by
vapour may be altered by raising or lowering the tube in the rc-
<ir, and changes of temperature may be produced by sur-
rounding the upper part of the tube by a glass cylinder, «/, about

inches in diameter and fourteen inches in length. This cy-
linder is closed at both end- with cork, through which the tube
:ul may be filled with water at different temporal;,

iltering the temperature and volume occupied by the vapour
we obtain the following results :

(i.) If, while the temperature remains constant, we increase the
volume, then

(a.) As long as there is liquid in excess above the mercury to
furnish fresh vapour for the increased space opened for its recep-
tion, the elastic force, as measured by the depression of the mer-
cury, and consequently the density of the vapour, remain constant.
The density of vapour in contact iritli if* //y///i/ depends, therefore,
, mi its temperature, and is independent of the volume occu-
j'i.-d by it. This density is called the maximum density at the <>'

(/3)» When the liquid above the mercury is all evaporated.
the elastic force and density diminish on increase of volume, as

in permanent jja-es; and it' the volume !>,> a^ain reduced, the elas-
• ree and den-itv increase until the latter attains the maximum
to the temperature. The eilect of any further diminution of
volume is t" reduce a portion of the vapour to the liquid state.*

of density and elastic l'..rce in vapour separated
liquid are generally assumed to I'.. How Mar'n'tte's law. up
to the point of maximum density; this is true while the vapo:
still at -oiiH- di.-taiiec from this point, hut on Approaching it the
if found to increase more rapidly than the ela--
• roliablv owini: to a partial condensation of the particles
.ipour through its mass. We will return to this subject in
n on the density of vapours.

* As we have assumed the temperature momentary change oft. MI|M -r.-uun -. li ..
to rein preceding rcaulu diaeipated, orreatoi UK ling bo-
are only true after Ihe heat developed by dies. V it also to be attended to
condensation or absorbed by expansion, in the .>

mge of volume, and vliirli • an--* a t-- 1» rniiiii. nt kraacs or vapours.

l6o LAWS OF VAPOURS. [BOOK I.

(ii.) If the space occupied by the vapour above the mercury
remains unaltered, then

(a). As long as there is liquid in excess, if the temperature
is raised, the density of the vapour already formed is increased by

-li vaporization, and the elastic force is consequently increased
in a much more rapid ratio than it would be in a permanent gas,
by the same change of temperature. Conversely, if the tempera-
ture be lowered, a portion of the vapour is condensed, and recon-
verted to the liquid state ; its density is diminished, and its elastic
force reduced more rapidly than in a permanent gas.

(/3). When the liquid is exhausted the elastic force increases
on increase of temperature, as in the case of gases, and diminishes
on its decrease, according to the same law, until the temperature
reaches the point for which the density of the gas is the maxi-
mum ; any further reduction of temperature is accompanied, as
was stated above, by a partial condensation of the vapour.

As Mariotte's law is assumed to apply to the changes of den-
sity and elastic force in vapours separated from their liquids, so
Gay-Lussac's law of the equal expansion of all gases and vapours
under all pressures, for the same change of temperature, is gene-
rally considered applicable under the same circumstances. The
investigations of MM. Regnault and Magnus on the expansions
of gases, however, render it very improbable that the coefficient of
expansion of any given vapour is the same under all pressures, or is
the same with that of air for different vapours at a given pres-
sure. But while we are ignorant of the true law which con-
nects the elastic force with the density, when the temperature
is constant, and of the relation between the increase of volume
and temperature under all pressures, we are obliged, in our
calculations, to assume the applicability of Mariotte and Gay-
Lussac's laws to the case of vapours separated from their liquids.
In the following investigation, accordingly, we shall proceed
upon this assumption, reminding the student, however, that all
results derived from it can be only considered approximately true.

1 09. General Properties of Vapours. B. In a Spacefilled with a
permanent Gas. — If the space over the liquid in the barometric
tube (Fig. 48) is occupied with air or any other permanent gas,
the laws of the formation of vapour, and of the relation between

CHAP. II.] LAWS OF VAPOURS. l6l

the density, tension, and temperature, are exactly the same as in
vacuo. The only difference between the two cases is this, that
while in vacuo the quantity of vapour requisite to saturate the
space open for its reception is formed instantaneously, time is re-
quired lor its production in a space occupied by a permanent gas.
The density and elastic force, however, of the vapour formed, are
the :> n vacua, and depend merely on the temperature ; and

accordingly the density and tension of the mixture of dry gas and
vapour are equal to the sums of the separate densities and tensions
ctively.

1 10. Relation between the elastic Force and Temperature of Va-
pours at their maximum Density; absolute Density of Vapour. — If
we rai-e the temperature of a vapour separated from its liquid,
and then diminish the space occupied by it, until the density
becomes the maximum due to the increased temperature, the rela-
tion between the elastic force at the former temperature and den-

. and at the latter, is the same as in the case of a permanent
gas. Hence, calling the elastic forces of the vapour at the two
temperatures/,/', and the corresponding densities d, d\ we have*

/= — I + at
~

a being the coefficient of expansion of the vapour for i° C.,

r, in the owe of a permanent gas, ^^ d> L±^t. If, n0w, th. :
•Oppose thf initial «-la<ti.- f-r.-.-, .1,-n-ity, ' + at

and temperature, to be/, rf, and t. ami aft- *•*»• "n, hanged, we o

any change of t. and volume, 8** ^ a quantity equal t.. that l.y wl.i.-h

•i-s become /, d, and t'. !t was expanded, so that it -hall r, turn to

suppose, in the first instance, the to original v,,l,m>, -an.l -1, -UMIV d~ we have

density alone to change, and become «f, *g*in, by Mariotte'a law, the new •
rail the corresponding elastic force 0, we
law, as the temperature
remains constant, ^ :/::</: rf, and there-

fore $ f'j- Next, suppose the temprra-

clarticforce, /'=/'rf'7' "in thetext- An<1 fur-
f, remaining unaltered, the fohmt«f A in ^ ^^^ W6 ^ ^ „

gas is thus increased in the ratio - —
anda< , density d. (/

icndtyrf-be- ^ at 0^, « A, we have/»Arf(, 4 a0.

^ gub6tituting ita ^m for ^

1 62 LAWS OF VAPOURS. [BOOK I.

which we will assume, according to Gay-Lussac's law, to be the
same as for dry air, assigning to the latter, however, the value
0.00366 determined by M. Regnault, instead of that given by
M. Gay-Lussac.

Since we have in general, in the case of gases, the relation

f=kd(i + at),

where k is a constant depending on the nature of the gas, being
the ratio of its elastic force to its density at o°, it follows that for
two different gases taken at the same temperature t, and under the
same pressure/, assuming a to be constant for all gases, we have the
relations

hence

d K

-y, = T = const. ;
a K

in other words, the ratio of the densities of any two gases under the
same pressure, and at the same temperature, is constant for those
gases, whatever be the temperatures and the pressures. And as we
have seen above that the relation between the elastic force of a va-
.pour and its density and temperature is the same as in the case of a
gas, it follows that the ratio of the density of any vapour to the
density of dry air, under the same pressure and at the same tem-
perature, is constant for that vapour. This ratio is called the
absolute density of the vapour, which may, accordingly, be defined
to be the ratio which the weight of a given volume of vapour bears
to the weight of the same volume of dry air, under the same pressure
and at the same temperature.

in. Density of a Vapour referred (i°) to dry Air, at a deter-
mined Temperature and Pressure, or (2°) to its own Liquid at a
given Temperature. — If we represent this absolute density of a
vapour by the symbol m, and by d and A the densities of vapour
and dry air at the same temperature t° and pressure/, referred
to any fixed standard, we have

d = mA ;
but (no)

A _ / i + at'

CHAP. II.] LAWS OF VAPOURS. 163

A' being the density of dry air at t* and/*. Hem •<•

., f l +at

which gives the ratio of the density of a vapour, at any tempera-
ture t and elastic force/, to the density of dry air at any assigned
temperature and pressure.

( i°). If we adopt as the standard of density the density of dry
air at the temperature of o° C., and under a pressure equivalent
to a column of mercury 760""" in height, we have

.

760 I

where the force/ of the vapour should be expressed by the height
in millimetres of the mercurial column which it would sustain.

(2°). It is, however, more convenient, in some cases, to assume
as the standard of density the density of the liquid from which
the vapour is produced, at some determined temperature. In the
case of aqueous vapour this temperature is generally either o° C.,
or that of the maximum density of water, viz., 4° C. ; and the
ity of dry air at the temperature of o°, and under the pressure
ui' 760""°, referred to the latter standard, being 0.001293187,*
it is necessary to substitute these values for A'9 S, and/, and also

ui its value, which, as we shall see hereafter, is 0.622. By these
:itutions we finally obtain

d = o.ooo ooi 058 ^ ,
I + at

if the elastic force is expressed in millimetres of m»'ivmy, and the
temperature in centigrade degrees. But if we express the elastic

in Knglish inches, and the temperature in decrees Fahivn-
thc formula becomes

d = o.ooo 026 812

• •'jii.d f» 0.00203. Ht-ner if v. » the ratio

•luinc of vapour, at f ' Falir, iind /

••• M. Regnauli. tin- while UM weight of th« Mine volmn
MO litre of dry air at o' ami till.«| wnt.-r •! . «» looogrs.

760"" b oqual to 1.293187 prammr-s — Mcmoircf >i

164 KXPKKI.MKMAL RESEARCHES ON [BOOK I.

of mercury), to the volume of water at 39° F., from which it was
produced, we have

p = 37296.7

•

112. Connexion between elastic Forces and Densities. — It fol-
lows that if we know the density of a vapour, referred to a given
standard, at any one temperature t\ and the elastic forces at all
temperatures, we can determine, by means of the preceding equa-
tions, the density, referred to the same or any other fixed stan-
dard at any assigned temperature ; and conversely, if we know
the elastic force at one temperature, and the densities at all, we
can calculate, from the same equations, the elastic forces at all
temperatures. For knowing the density of a vapour at Z'°, and
its elastic force /', and dividing the former by the density of dry
air, at the same temperature and elastic force, referred to the same
standard, we obtain the absolute density, m, and then, by the method
indicated in the preceding paragraph, we can obtain the density,
referred to any fixed standard, at any assigned force and tempera-
ture, or the elastic force at any assigned density and temperature.

The series of elastic forces and densities corresponding to dif-
ferent temperatures, therefore, being thus related, if either be
determined by experiment, the other can be ascertained by cal-
culation. Such calculated values, however, being obtained on
the assumption of the applicability of Mariotte's and Gay-Lussac's
laws to the case of vapours, can only be regarded as approxi-
mately true ; and to obtain accurate results, both the elastic forces
and the densities corresponding to different temperatures should
be made the object of direct experiment.

We proceed to point out, in the following sections, the princi-
pal methods which have been adopted by various physicists for
the experimental investigation of those quantities, and first of the
methods of determining the elastic forces of vapours of various
liquids, at their maximum density for the temperature.

SECT. IV. — EXPERIMENTAL RESEARCHES ON THE ELASTIC FORCE OF

VAPOURS.

113. M. Zleglers Experiments.— The earliest experiments on
this subject appear to have been made by Ziegler, a Swiss, who

CHAP. II.] THE ELASTIC FORCE OF VAPOURS. 165

published them at Basle in 1769, in a treatise entitled " Speci-
men physico-chemicum de Digestore Papini, ejus Structure,

ctu, et Usu, primitias Experimentorum novorum circa Flui-
clorum a Galore Rarefactionem et Vaporura Elasticitatem exhi-
bens." His apparatus consisted of a kind of digester formed of
copper, and strengthened externally by iron rings or hoops. In
the lid was fastened a short tube, open above and closed below,
which contained oil, mercury, or fusible metal, and a thermome-
ter placed in this indicated the temperature of the water in the
digester. The elastic force of the vapour was measured, up to a
certain amount, by the column of mercury, whose weight balanced
its pressure; beyond that, by a weighted lever arm acting on a
safety valve in the lid of the digester. As M. Ziegler allowed
the space above the water at the beginning of the experiment to
remain full of air, the elastic force of the latter was added to that
pour, and accordingly his experiments wore made, not
on pure vapour, but on a mixture of vapour and air.

114. M. Betancourt's I • nts. — Shortly after M. Ziegler's

•ri merits, but without any previous knowledge of them,
M. Betancourt, an ingenious Spanish phvsieist. investigated the

ic force of the vapours of water and spirits of wine, and laid

csults before the Academy of Pui is who published his me-
moir in the year 1790, in the '• Mem. .ire- - run-
Hi- apparatus consisted of a small copper boiler, a
inches in width by fourteen deep, which contained in its
lid three opcn'mus; through one of these the liquid was intro-
••«!, the stem of the thermometer, whose bulb was immersed in

. apour or fluid in the boiler, passed in a steam-tight collar
through the second, and the third was connected with |

iHiiin<_r tin- elastic force of the vapour. In the u;
:d«- of the boiler was inserted a mill- with a stop-
cock. MS of which communication could l>e made with an

ump, tor the purpose of rxhau-tin;: the air from the appa-

icd as perfect a vacuum as possible, and <
.id to o° by means of meltin .. • . M : ,mt

observed, in the case of water, a diil'eience «.f Icv.-l in the n

the manoin.-ter. amounting to 0.3" 1'Veneh inch.

1 66 EXPERIMENTAL RESEARCHES ON [CHAP. II.

Knowing that the vacuum in the apparatus was not perfect, and
having no means of ascertaining the exact amount of air remaining,
and feeling convinced that the clastic force of aqueous vapour at o°
must be very small, M. Betancourt came to the conclusion that
he would approximate most nearly to the truth by attributing the
whole of the force at o° to the remaining air. He accordingly
subtracted the height of the column which measured it, namely,
.375 inch, from the heights corresponding to all higher tempera-
tures. It appears, however, as we shall see presently, from Mr.
Dalton's investigations, that the elastic force of aqueous vapour
at o° is equal to .2 of an English inch, or .188 of a French inch,
and that consequently the difference between this and .375 inch
is all that M. Betancourt should have attributed to the presence of
air. In order to compare his results, therefore, with M. Dalton's,
we should add the quantity .188 to the heights of the mercurial
column, as given by him, corresponding to different temperatures.
115. M. Voltcis Experiments. — In 1 793 Volta published in Brug-
natelli's Journal some experiments on the dilatation of air, which
he determined to be i -f- 213 of its volume at o° for each degree
of Reaumur, a result agreeing very closely with that subsequently
assigned by M. Gay-Lussac. He also made some investigations
on the elastic force of aqueous vapour, which were subsequently
given by Sr. Moretti, in a Supplement to his translation of Kla-
proth and Wolff's Chemical Dictionary. Volta's apparatus was
similar to that subsequently employed by Dalton. He assigned
the force of two French lines, or 0.167 °^ a French inch, to
aqueous vapour at o°, a force not differing very much from that
given by the English physicist. From his observations of the forces
at other temperatures, Volta derived the law, that the increments
of the elastic forces, starting from o°, form a simple geometric
series, whose first term is 0.36 and ratio i.i i, the corresponding
temperatures constituting an arithmetic series, whose first term is
o°, and common difference 2° R., the forces being expressed by
the height of mercury in lines which the vapour would sustain at
o°. To derive from this the corresponding elastic force at the ac-
tual temperature £, the force as determined above must be multi-
plied by ( i + - — J, according to the value assigned by Volta for

(HAP. II.] THK ELASTIC FORCES OF VAPOURS. 167

the coefficient of expansion of air, supposed also to be the same
for vapour. Thus the force at o° being 2, that at 2° R. = 2 + 0.36,
that at 4°= 2 -1-0.36-1-0.36 x i.n, &c.

1 1 6. Dr. Robinson's Experiments. — The Encyclopaedia Britan-
nica (1797) contains, under the article " Steam," furnished by
Dr. Robinson of Edinburgh, a table of the elastic forces of aqueous
vapour for every 10° F., from 32° to 280° F. His apparatus was
similar to M. Betancourt's, and, like him, he also considered the
force of vapour at 32° F. as equal to o; by adding its true force
at this temperature, his results approach more nearly to those of
Dalton below 212°.

1 17. Mr. Dalton n l-.i'i" r'nn cuts. — Mr. Dalton's researches were
communicated to the Manchester Society in the year 1801, and
published in their Memoirs in the following year. He extended

•bservations on aqueous vapour from 32° F. to 212° F. As
as 150° he employed the apparatus described in page 158,
raising the temperature of the water in the surrounding cylinder
to that temperature; for higher temperatures he used a tube bent
as a syphon, having the shorter arm sealed and filled with mer-
cury. Into this he introduced a small quantity of water above
the mercury, and surrounded it with a double cylinder of tin, for
holding the hot water or oil, as in Fig. 50. The force of tho
aqueous vapour depressed the mercury by a quantity which could
be ascertained by the equal amount of elevation observed in tho
longer arm. Mr. Dalton employed this latter form of apparatus
also to determine the elastic forces of vapours from other liquids
than water, which, at temperatures below 150°, equalled or sur-
passed the atmospheric pressure, and for which, accordingly, the
first form was unsuitable. The observations made by thr.-e
forms of apparatu M I > ilt>m verified l.y the method reierred to
JMJKII/'- i.\i, based on tin- principle, that when liquids enter into a
state of ebullition, the elastic force of their vapours equals tho
to which they are submitted. The result- obtained |.v
method airi' :ly with tli< tlie two

fonn

•r repeated experiments and careful « -n of the

M I > ilton states, he arrived at the conclusion, that

the- ices of aqueous vapours, f< atures ascending

1 68

EXPERIMENTAL RESEARCHES ON

[BOOK I.

from 32° by intervals of 1 1 J° F. or 5° R., are represented by the
terms of a geometric series, whose ratio is not constant, but di-
minishes for each term by a quantity whose mean value is 0.015,
or rather 0.01567, in proof of which he gives the following
Table.

Temperature.

Forces in English Inches.

Ratios.

32°

.200

1.485

43i

.297

.465

54|

•435

•45

.630

•44

77

.910

•43

88^-

1.290

99i

1.820

.41

nof

2.540

.40

122

3.500

•38

133!

4.760

•36

H4*

6.450

•35

055J

8.550

•33

167

11.250

•32

178!

14.600

•30

l89i

18.800

.29

2 oof

24.000

.27

212

30.000

•25

By means of the law announced above, which he assumed to
hold good below 32° and above 212°, Mr. Dalton extended his
table, by calculation, beyond the limits of his experiments, to
-40° F. and + 325° F., taking as the successive ratios below 32°,
1.500, 1.515, &c., and above 212°, 1.235, I-220» &c-

On comparing the elastic forces of vapours of different liquids
at various temperatures, Mr. Dalton was led to the conclusion,
that the vapours of all liquids have equal elastic forces at tempe-
ratures equidistant from those of ebullition, — points at which they
have a common force equal to the atmospheric pressure. This law
has been shown by M. Despretz to be approximately true, within
certain limits, for water, ether, and alcohol, but to fail in the case
of essence of turpentine and other liquids. Although only ap-
proximately true, however, it serves to explain why liquids
which boil at high temperatures, as mercury and sulphuric acid,

CHAP. II.] THE ELASTIC FORCE OF VAPOURS. 169

produce vapours which are scarcely sensible at ordinary atmos-
pheric temperatures; for if the law were strictly true, the force
of mercurial vapour at 15° C., which is 345° C. below its boiling
point, should be equal to that of water at a temperature equal to
100 - 345 = - 245° C. ; and the force of vapour of sulphuric acid
ut the same temperature, which is 295° C. below its point of ebul-
lition, should equal that of water at 100 - 295 = - 195° C. : but we
have reason to believe that the elastic force of vapour of water is
insensible long before it reaches so low a temperature as either
of those.

1 1 8. M. Gay-Lussacs Experiments. — After Mr. Dal ton's expe-
riments, which, as we have seen, extended from o° to 100° C.,
we have next to notice some made by M. Gay-Lussac for the
purpose of ascertaining the force of vapours at temperatures below
o°. His apparatus consisted of a barometer tube bent as in Fig.
49, into the upper portion of which was introduced a small quan-
tity of the liquid whose vapour was to be examined, as in Mr.
Dalton's experiments. The requisite temperature was produced
by plunging the bent portion of the tube into a freezing mixture,
whose temperature was indicated by the small thermometer in A.
The pressure of vapour then in the vertical tube was equal to
that in the coldest part of the bent portion, for the different strata.
of vapour from the surface of the liquid to the mercury, resting
one upon another, could none of them sustain a greater pressure
than that due to the coldest stratum, namely, the one in contact
with tin- liquid. Practically, in fact, if vapour of a higher tension
or was generated from a small quantity of liquid in the
tube, it would expand into the bent arm AB,
where the pressure was less, and there would be constantly con-
drn-c'l, until all the liquid in th<- vertical part was evapora
and moreover, all through this process the pressure on tin- iui

:y would only be equal to the reaction of the stratum

i r of lowest ten Mon. I: of this apparatus M .<

Luino determined th. !'.. ice of vapour of ice at - i9°.59C., which

1 to be equal to imm-353 or 0.0533 °j<:m ''-"^h-h inch,

which w.uild differ very lili! .111. d by

(
Z

l~0 EXPERIMENTAL RESEARCHES ON [BOOK I.

that law the force .06570, thus proving that the continuity of
the law of the elastic force of aqueous vapour is not interrupted
by the solidification of water.

1 19. Mr. Ure's Experiments. — In the year 1818 Mr. Ure pub-
lished* a series of experiments on the elastic forces of different
vapours through an extensive range of temperatures. The appa-
ratus which he made use of was similar to that form of Mr. Dai-
ton's represented in Fig. 50, except that he measured the elastic
force of the vapour above the mercury in the closed portion, by
the height of the column which it was necessary to add in the
open branch c, to maintain a constant level ab in the closed one.
In this way the experiments were capable of being conducted
with greater facility at different temperatures, as the portion of
the tube to be heated or cooled was of constant length, and the
same form of apparatus answered for all temperatures.

Mr. Ure sought to represent his results by a law similar to
Mr. Dalton's. He gives as the successive ratios for intervals of
10° F. starting from 210° upwards, 1.23, 1.22, 1.21, decreasing
by the common quantity o.oi, and for the divisors descending
from 210°, 1.23, 1.24, 1.25, &c. To preserve the continuity of
the law, however, as 1.23 is the factor for the change from 210
to 220, 1.24 should be the first divisor descending from 210 to
200, 1.23 the next, and so on.

Mr. Ure also extended his researches to the vapours of alco-
hol, ether, petroleum, and oil of turpentine.f

1 20. M. Despretz's Experiments. — In a memoir read to the
Institute in November, 1819, M. Despretz undertook to examine
specially the correctness of Dalton's law relative to the equality
of elastic forces of vapour at temperatures equidistant from their
boiling points. This law he found, as we have mentioned above,
to be only approximately true in the case of alcohol and ether,
as compared with water, within certain limits, and to fail altoge-
ther with turpentine and other liquids. In proof of this he gave
the following results.

* Philosophical Transactions, 1818, Part ii., p. 338.
t Ibid., p. 358.

CHAP. II. "|

THE ELASTIC FORCE OF VAPOURS.

Temperature.

Temperature.

Iiu-reo.se of

Temperature.

Dem-a<eof

Nome of Liquid.

Elastic Force

F.lu>tic Force

T«-ni|.vrn-

Elastic Force

Tempera-

= ojn.76.

-I-.I4.

ture.

= o".38.

tun-.

Water, . . .

IOOC.O

no°.o

I0°.0

84°.6

iS°-4

Alcohol, . .

78.7

89.4

10.7

63 .8

14.9

Ether, . . .

35-5

47-5

12 .0

(17-77)

(17-7)

Turpentine,

156.5

174.1

17.6

134-4

22 .1

From this we see that the numbers in the fourth and sixtli
columns, which, if Dalton's law were true, should be equal, agree
very closely for alcohol and water, less nearly in the case of ether,
but are altogether discordant for turpentine. M. Despretz found
that this law signally fails also in the case of a liquid formed of
chlorine and olefiant gas, and M. Marx* of Brunswick has found
a similar result in the case of sulphuret of carbon.

121. Experiments of MM. Didong, Arago, fyc. — The next se-
ries of experiments relative to the force of aqueous vapour, to
which we will direct the attention of the student, was a most im-
portant one, made in the year 1829 by a Commission of the
;emy of Paris, consisting of MM. Prony, Arago, Girard, :ind
Dulong.f The object of this series of experiments was to deter-
mine the elastic forces of vapour at higher tensions than had yet

i observed, and the Commissioners accordingly pursued their
investigations as far as the temperature 224°. 15 C., the elastic force
corresponding to which they found to be equal to 23.934 atmos-
pheres, or a column of mercury at the temperature of o° of 18.19
metres, or 716.07 inches in height. The following is a brief de-
i of the apparatus employed by the Commissioners.

I apparatus was composed of two distinct parts, the one
intended for the production of the vapour, and the detennin::
of its temperature; the other !<>i the measure of its elastic force.
former consisted of a strong copper boiler, provided with a
safety valve «-. instruction, that \\' n it

by the excess of pressure of the vapour, a sliding weight on

:rm of its lever opened it c ly, and gave free egress to

i. In the upper plate of the boiler were scrun-d two

i-r (I., mi.l IM.x-
f Annalea dc Chimie et <le Physique, tutm . (1830).

172 EXPERIMENTAL RESEARCHES ON [BOOK I.

gun barrels, open above and closed below, one reaching nearly
to the bottom of the boiler, the other only extending about one-
fourth of its depth. These barrels were filled with mercury, and
were intended to hold the thermometers, which could not have
been exposed unguarded to the pressure of the steam, without
undergoing an alteration in the form and volume of their reser-
voirs which would have vitiated their indications. In order to
make the necessary correction for the portion of the instruments
unassimilated to the interior temperature, the stems above the
boiler were bent, as in Fig. 52, at a right angle, and a current of
water at a known temperature was kept constantly in motion
along them. The vapour ascended through the tube dd', where
it acted on the extremity of a column of water in the inclined
pipe d'd", which transmitted its pressure to the apparatus designed
for measuring its force. This column of water was kept at a con-
stant temperature bv means of the stream flowing round it from
the reservoir v, and the vapour, on reaching its extremity at u>
was constantly recondensed, and fell back into the boiler.

The apparatus for measuring the force of the vapour consisted
of a compressed-air manometer, MN, the Commissioners having
previously verified Mariotte's law by direct experiment as far as
a pressure of twenty-seven atmospheres. The vapour exerted its
pressure through the column of water in the pipe dd'd", on the
surface of the water in the reservoir, and so through the mercury
in the tube MN, on the compressed air in its upper portion. The
variable height of the mercury in the iron reservoir/ was seen in
a glass tube £, whose lower extremity communicated with tlic
reservoir, and its upper with the water in the pipe dd'd". The
air and column of mercury in the manometer were kept at a
constant temperature by a current of water flowing round it.

The experiments with this apparatus were thus made. The
water in the boiler was maintained in a state of ebullition for fif-
teen or twenty minutes, with the safety valve open to get rid of
all air both in the boiler and in the water itself. The valve was
then closed, the supply of water round the pipe d'd", was regu-
lated, the furnace was supplied with a determinate quantity of
fuel, and when the ascent of the thermometer and of the mercury
in the manometer became very slow, their indications were ob-

CIIAP. II.] THE ELASTIC FORCE OF VAPOURS.

'73

served and registered, until they reached their maximum. The
observations made at this last point alone were employed as the

B of the calculation of the forces and temperatures, those pre-
ceding and following serving only to guard against errors in the
readings.

The following table gives the results of the more trustworthy
of the Commissioners' experiments, after all necessary corrections.*

Elastic Force in Metres of

ury at o .

Elastic Force in Atmospheres
of o">.76.

Corresponding Temperature
observed.

1.62916

2.140

i23°.7 C.

2.1816

2.8705

'33-3

3-4759

4-5735

149.7

4-9383

6.4977

s

163 .4

5.6054

7.3755

168.5

8.840

11.632

188.5

13.061

17.185

206.8

I3-137

17.285

207 .4

14.0634

18.504

210 .5

16.3816

21-555

218 .4

18.1894

23-934

224.15

From these results, by a formula of interpolation which will
be afterwards given, they calculated the following tables.

TABLE of the elastic Force of Steam from i to 24

cording to ti I rs.

ac-

T,,n,H-

r.ituiv.

DM*

:

tur.-.

Ehrtk

Ti-MI|"T.I-

ture.

DMCk

I--..IV...

!.ini>.T.i

\

li

100°

I*

I»l

156.8

10

1 1

181.6
1 86.0

18
«9

209.4

2

12 1.4

6

160.2

12

190.0

20

*4

135 '

6J

7

'4

21
22

3i

140.6

7i

169.4

200.5

23

4,

8

172.1

16

203.6

4 .

I4.M. |

177. 1

17

206.6

Tl

* Ann.

'74

EXPERIMENTAL RESEARCHES ON

[BOOK i.

TABLE from 25 to 1000 Atmospheres.

Elastic

Tempe-

Elastic

Tempera-

Elastic

Tempera-

Elastic

Trm]HTU-

Force.

rature.

Force.

ture.

Force.

ture.

Force.

ture.

25

226.3

45

259-5

300

397-6

700

478.4

30

236.2

5°

265.9

400

423'5

800

492.4

35

244.8

100

3"-3

500

444-7

900

505.1

40

252.5

200

363-5

600

462.7

1000

516.7

122. Experiments of American Commissioners. — About the year
1836 a Committee of the Franklin Institute of Pennsylvania*
was appointed, at the instance of the Government of the United
States, to inquire into the causes of steam boiler explosions. In
the course of their inquiries they instituted a series of experi-
ments on the elastic force of steam at high pressures. The appa-
ratus which they employed was similar in its construction and
plan to that of the French Commissioners. Their experiments,
of which the following table gives the mean results, as determined
from a graphic representation of the actual results, were carried
as far as a pressure of ten atmospheres. For the purpose of com-
parison with the table of the French Commissioners, we give the
temperatures in both Fahrenheit and Centigrade degrees.

TABLE of elastic Forces of Steam, from one to ten Atmospheres,
according to the American Commissioners.

Pressure

Temperature.

Pressure

Temperature.

Pressure

Temperature.

in
Atmos.

Fahren.

Centigr.

in

Atmos.

Fahren.

Centigr.

m

Atmos.

Fahren.

Centigr.

I

212°

100°

4

298°.5

1 48^.0

8

336

i68°.9

4

235

I I 2.8

5

3°4-5

151 .4

H

340-5

171.4

2

250

121. 1

si

310

154.4

9

345

'73-9

»i

264

128.9

6

3*5-5

'57 -5

9i

349

176.1

3,

275

'35-0

6*

321

1 60 .5

10

352.5

178 .0

3i

284

140.0

7

326

163.3

4

291.5

144.2

7*

331

166.1

Journal of the Franklin Institute, vol. xvii. p. 289 (1836).

CHAP. II.] THE ELASTIC FORCE OF VAPOURS. 175

123. M. Magnus Experiments. — We have next to notice a
memoir on the expansive force of steam, by Professor Gustav
Miis, which appeared in PoggendorfFs Annalen, No. 2, for
1 844, and of which a translation has been published in the fourth
volume of Taylor's Scientific Memoirs. In this memoir the au-
thor, after noticing the defects in former methods, arising from
the difficulty of determining with accuracy the true temperature
of the vapour, and also the correct pressure, owing to the unequal
heating, and consequent partial expansion of the mercurial co-
lumn, proceeds to explain the method which he adopted to ob-
viate these difficulties.

In this method the vapour was generated in a U-shaped vessel,
adeb (Fig. 53), about four inches long, one end of which was closed,
and blown into a ball to increase the space for vapour, the other
was united with a long glass tube, be, by means of which connexion
was made with an air-pump. The closed end having been filled
with mercury which had been well boiled, some water which had
been boiled violently for half or three-quarters of an hour was
poured into the open end, and while still warm a small quantity
of it was conveyed, by inclining the tube, over the mercury in
bulb, and the remainder of the water in the open end was
then removed. To measure the elastic force of the vapour gene-
1 in the bulb at any temperature below 100° C., the open
end of the tube was connected with the air-pump, and the air
contained in it was rarefied until the mercury stood nearly at the
level in both branches. The elastic force of the vapour
was then measured by the height of the mercury in the barome-
ter gun Lr 'd to the air-pump, increased or diminished by
the small difference of level in the U-shaped vessel, both heights

•^corrected for temperature, the thin stratum of unvapor
water being also taken into account, an<l oxjuvssed by its e<jiii-
M t height of mercury. The temperature was M 1 by

enclosing the whole of the U-shaped vessel in a ca

!>out lourteen inches long and wide, and ten hi^li,
•unded l>y three similar cases, so that b< .eh two then-

ted a stratum of air five-eighths of an inch thick on all sides,
-c cases were suspended in one another to avoid all metallic
contact. The ,,utrr ease was heated by two nrgand lamps, which,

176 EXPERIMENTAL RESEARCHES ON [BOOK I.

when placed at a constant distance, and burned with a moderate
flame. M. Magnus found to yield a constant quantity of heat, and
thus to preserve the inner case at an invariable temperature.
The temperature was measured by an air thermometer whose re-
servoir, xyzy was fork-shaped, and enclosed the vessel contain-
ing the vapour ; its stem passed through the metallic cases on
one side, as the tube leading to the air-pump passed through
the other. Two mercurial thermometers, v, 10, also were intro-
duced through the lids of the cases into the inner space.

1 24. M. Regnaul£s Experiments. — It only remains for us now
to notice the very valuable memoir of M. V. Regnault on the
" Elastic Forces of aqueous Vapour," first published in the An-
nales de Chimie et de Physique for July, 1 844,* and since more
fully in the Memoirs of the Institute.-)- " To establish a phy-
sical fact," says this ingenious and accurate physicist, " we must
not confine ourselves to a single method of investigation. It is
necessary to employ various methods, and even to repeat those
made use of by former experimenters, unless they are absolutely
faulty ; and we must show that all, when used with proper pre-
cautions, conduct to the same result, or if this be not the case, we
must point out by direct experiment the causes of error in the
defective methods." Acting on this principle, M. Regnault re-
peated the methods of Dalton, Ure, Magnus, Dulong, and Arago,
with such modifications as the improved state of experimental
science and his own skill and experience suggested, and has
pointed out the defects under which they labour, and the limits
within which their results may be relied upon.

Mr. Dalton's method may be described as consisting essentially
in determining the heights of the mercurial column in two baro-
meter tubes, the chamber of one being occupied with vapour, and
the other being a vacuum. In this method the temperature of
the vapour is determined by that of a water bath surrounding the
chamber, and either the whole or a part of the mercurial column
is maintained by the same means at the same temperature. M.
Biot has remarked that the chief defect in this method arises

* Ann. de Chim. et de Phys. (3™ Serie), tome xi. p. 273 (1844).
f Memoires de 1'Institut, tome xxi. p. 465 (1847).

CHAP. II.] THE ELASTIC FORCE OF VAPOURS. 177

from the fact, that it is impossible to maintain the water surround-
ing the tubes at a constant temperature through all its depth, if
this depth is considerable, and its temperature differs much from
that of the surrounding medium. Mr. Ure attempted to remedy
this defect by limiting the space occupied by the vapour, and
thus reducing the depth of the bath, and in this respect certainly
his modification of Mr. Dalton's method was a decided improve-
ment. M. Regnault has shown that if the whole of the tubes be
surrounded by water, for the purpose of maintaining the columns
at the same known temperature, Mr. Dalton's method is capable
of giving accurate results between the limits + 10° C., and + 30°
C., provided the water be incessantly and rapidly agitated, the
agitation being merely interrupted for a moment to observe the
heights of the mercurial column. Above the higher limit, how-
ever, the separation of the liquid into strata of unequal tem-
perature commences the instant the agitation ceases, and the
observations are accordingly rendered uncertain.

Where it was intended only to raise the chambers and a part
of the mercurial column to the temperature of the vapour, M.
Regnault made use of the following form of apparatus.

(i.) Two barometers, as similar as possible, of about fourteen
millimetres internal diameter, are arranged side by side on a frame,
55). These barometers pass through two tubular open-
in the bottom of a vessel, vv', of galvanized sheet iron, and
are secured by means of caoutchouc collars. The ve- ! \\ .
whose horizontal section is given in Fig. 57, has on one side a
:iiLrnlar aperture, round which is fixed an iron frame. A
plate of glass with perfectly parallel faces is secured to this
•ans of a similar Iran .«•«! t«» tin1 former by

screws. A slip of caoutchouc, of tin- form of tin- c-'ntonr .'I
aperture, is placed l>etw.-m the glass and tin- fra; and

oint perfectly water-tight. The two 1 (ammeters arc
plim^'d in tin- M rTOlI r. Tin- capacity <.| the Vessel vv

is about forty-five litres. This vessel is filled with water which
is continually agitated, and its temperature is given by a \
sen*-! omial thermometer imi M it, whi.- nred

by ii ..ill horizontal tc!< 1 iit of the

column in tl ms of a kath-

2 A

178 EXPERIMENTAL RESEARCHES ON [BOOK I.

tli.- nuitatiim of the water being stopped for an instant at the time
of tin* observation of each column.

Observations are made with great precision at the tempera-
ture of the surrounding air; to observe the force at higher tem-
peratures a small quantity of water is removed from the vessel
by means of a syphon, and replaced with a corresponding quantity
of hot water. A spirit lamp is then placed under the vessel, and

listance from it, as well as the height of its wick, is so ar-
ranged, that the temperature of the water, which is still kept in
a state of brisk agitation, finally becomes constant. This condi-
tion is easily attained after some trials, and if the temperature does
not surpass 50° C., it may be maintained stationary and uniform
for any length of time, provided only that the agitation of the
•water is brisk and constant. Three or four observations were
made every time that the temperature was rendered stationary,
an interval of eight or ten minutes being left between each. In
this method of operating, the portions of the columns outside the
vessel vv' are in circumstances completely identical, and the
difference of height of the portions within, which are at the tempe-
rature of the bath, being reduced to o°, measures exactly the ten-
sion of the vapour, allowance, of course, being made for the pres-
sure of the film of water. It is unnecessary to point out how
much more accurate this method of ascertaining the temperature
corresponding to observed forces is, than either M. Betancourt's
or Mr. Dalton's.

(ii.) A second series of experiments M. Regnault made with
the following apparatus. A balloon, A (Fig. 55, 56), whose capa-
city equals 500 cubic centimetres, contains a little glass vessel full
of water recently boiled. The balloon is soldered to a curved tube
cemented into a tubular piece of copper with three branches, d, e,f.
In the branch e is cemented a tube soldered to the upper part of
the barometer h, and in the branch / a tube communicating with
an air-pump, by means of the desiccating apparatus MN, filled with
powdered pumice steeped in sulphuric acid. The tube o is a
perfect barometer, as before. The apparatus being arranged as
in the figures, a vacuum was made forty or fifty times succes-

ly, and each time the air slowly re-admitted; by this means
the interior of the balloon and barometric chamber was com-

CHAP. II.] THE ELASTIC FORCE OF VAPOURS. I ~U

ly dried. The vacuum was then finally made as perfectly
as possible, and the tube fl sealed by a blow-pipe. At first M.

unable to reduce the vacuum below two millimt :
but his air-pump having been cleaned, he subsequently succeeded
in bringing it frequently below imm. The balloon was then
surrounded with melting ice, and the difference of the columns in
the two tubes gave the elastic force at o° of the remaining air.

ice having been removed, the vessel vv' was filled with water,
and its temperature being sufficiently raised, the little glass vessel

! >urst by the expansion of the water it contained, and the bal-
loon and chamber filled with aqueous vapour, whose force at the
corresponding temperatures was observed as before.

This method answers very well for temperatures below that
of the surrounding medium, and for 10° or 15° C. above it; it also
answers for determining the force of aqueous vapours in air of
any density, within those limits of temperature.

(iii.) Those two forms of apparatus do not answer for tensions
above 200 millimetres; beyond this force M. Regnault employed
the following, which in principle is similar to Professor Magnus's,
and which he also employed in the case of liquids more volatile
than wat

A -vphon-shaped tube, ale (Fig. 59), of about \$mm internal
diameter, terminates in a fine curved tube, ce. The closed branch

tilled with mercury, which is carefully boiled to expel all air
and moisture. When the mercury is cool a small quantity of vo-
latile, liquid is introduced into the branch be, and boiled
minutes; the tuh«- is then inclined, and a little of tin- liquid, yet
.tssed up into the branch r//> ; the branch /'<• is then com-
pletely dried. Tin- tube is now fixed in a pei :

:i in the \e-el vv , iii front of t lie glass plate. The tube ce

18 cemented into one branch of a pieee nf mpprr, «//', who-e other

commni. . with a manomelric apparatus with

• p-COck r i. and the other, /', with an air-]>uni]>, if

ssary. The tul.es ///, // are lii>t completely filled with mer-

. the air be' lied throng!. - is then

'1 with the blo\\ -pipe, and a p
lowed to llow out through the |fc>] . the pi. the

180 BXPKKIMKMAL KKSHARCHES ON [BOOK I.

air in the branch nee is so far diminished as ultimately to become
nearly equal to the pressure of the vapour in am, when the mer-
cury in the two branches of the syphon-shaped tube falls nearly
to the same level. The force of the vapour is then measured by
the atmospheric pressure, diminished by the column a)3 in the
manometer and the column mn in the tube ab, both these co-
lumns, whose temperatures are known, being reduced to their
heights at o°. The temperature of the vapour is ascertained as
in the preceding experiment.

(iv.) None of the foregoing methods answer for temperatures
above 60° or 70° C. At higher degrees the water in the vessel
vv' separates so promptly into strata of different temperatures, as
to require constant agitation to prevent this result from taking
place. For temperatures above 100° C., moreover, those me-
thods become impracticable from other causes. For higher de-
grees, therefore, M. Regnault had recourse to the well-known
method employed by Mr. Dalton and other physicists subse-
quently, of ascertaining the temperature of the vapour of water
boiling under determined pressures.

In order to obtain results of the degree of accuracy which
this method is capable of giving, it is necessary to boil the water
in a vessel communicating freely with a space of tolerable capa-
city, in which we can dilate or condense air at will, and by this
means form an artificial atmosphere, which exerts a determined
pressure on the surface of the heated liquid. We thus obtain a
temperature of ebullition as perfectly stationary as that of water
boiling in free air, and we can maintain this temperature station-
ary as long as we will. The apparatus employed for this purpose
by M. Regnault is represented in Fig. 60.

It consists of a retort of red copper, A, closed with a cover.
Tliis cover carries four iron tubes, closed below; of these, two
descend to the bottom of the retort, the others only reach half
way down. These tubes, which are 7""" in internal diameter,
and about imm thick, are surrounded by a case of very thin
copper attached to the cover, and having apertures, o, o, o, in its
upper part. They are filled with mercury to within a few cen-
timetres of their upper edge, and hold four mercurial thermome-

CHAP. II.] THE ELASTIC FORCE OF VAPOURS. l8l

ters, whose bulbs descend to the bottom of the tubes. From the
arrangement of the tubes it appears that two of the thermom<
are plunged in vapour, and two in water (Fig. 61).

The neck of the retort is connected with a tube, TT', about
one metre in length, surrounded by a copper cylinder, through
which Hows a constant current of cold water, supplied by a re-
servoir P. This tube communicates with a copper balloon, of
about twenty-four litres in capacity, contained in a vessel, vv .
full of water at the temperature of the surrounding medium. To
the balloon is attached a pipe with two branches, one of which is
cemented to the tube egh, of the apparatus represented in Fig.
56, when the experiments are made at pressures inferior to that of
the atmosphere, or with the tube pq of the apparatus in Fig. 62,
for greater pressures. The second branch is connected by means
of a lead tube, #', with an exhausting or condensing air-pump.

For pressures inferior to the atmospheric, the air in the bal-
loon having been rarefied, the water in the retort is heated until
ebullition commences. The vapour, according as it forms, is
condensed in the refrigerator TT', and falls back into the retort.
The pressure is measured by the difference of heights of the mer-
cury in the tubes ha and o. It may be remarked, that the column
in the barometric tube 7m, connected with the balloon, is never
absolutely stationary; the amplitude of its oscillations, however,
when the fire is properly regulated, is very small, not cxeeedinu one-
tenth of a millimetre. The mercury in the barometer 0, on the other
hand, remains perfectly stationary. The difference of the heights
ofthc.-e columns is observed by means of a kathetmueter. and an
assistant at the same instant notes the height of the thennonn ••
Several otweTYfttioni were made, ut intervals ofei^ht or tin mi-
nute.-, under the >anie pre>-ure. and it was thus easy to peiv
ttCy «•!' the temperature.- indicated bv the t;
mon. :ime pressure, and to show that the lra-t ch;:

in the latter was followed by a correspondin in the

fora

height ..f the kathetnmetcrs not exceed i in.' one n
\\-\\v\: ices of level in the appara' . I

i. it wa> necessary to employ two ol'them.
In order to ascertain ii' the divinon- <>t the scales ol in-

1 82 EXPERIMENTAL RESEARCHES ON [BOOK I.

nonts were identical, M. Regnault read off the divisions of
in lengths of centimetres, by means of the other, and such
was the accuracy of their graduation, that he in no case encoun-
1 a difference of more than one-twentieth of a millimetre.
" To attain such a degree of precision in the measures, it is evi-
dent that the instruments must be constructed with the greatest
accuracy ; the telescopes must not have too great a focal length
(om-3o), and the levels, in particular, must possess extreme sensi-
bility. Those in the kathetometers constructed by M. Gambey
indicated inclinations of one second. The verniers gave directly
one-fiftieth of a millimetre, and easily admitted of the estimation
of one-hundredth."*

" The thermometers employed in the experiments made at
pressures inferior to the atmospheric ranged from o° to 100° C.;
they had from six to eight divisions in i° C. ; it was consequently
easy to read with certainty the one-sixtieth of a degree. Those
employed for higher pressures had a range from o° to 240°, and
i° C. contained 2.5 or 3 divisions of their scale. All these in-
struments were graduated and verified by ourselves with the
greatest care."f

In estimating the temperature from the indications of the
thermometers, a correction required to be made for the portion
of mercury in the stem unassimilated in temperature. The tem-
perature of this portion was ascertained by means of a sensitive
mercurial thermometer, suspended between the four stems. It
may be remarked that the temperature indicated by the thermo-
meter in the liquid was always higher, at low temperatures,
than that indicated by those in the vapour; the difference in
some cases amounted to o0.7. As the pressure approached the
atmospheric, this difference became less, and at high temperatures
was quite insensible.

(v.) The method J by which M. Regnault investigated the force
of vapours at high temperatures was similar to that last described,
and the apparatus which he employed for this purpose differed

• Ann. dc C'himieetdePhys., 3me Seric, J Memoires de 1'Institut, tome xxi. p.

tome xi. p. 311. 538.

t Ibid., p. 3.3.

CHAP. II.] THE ELASTIC FORCE OF VAPOURS. 183

from the preceding merely in the size and strength of the parts.
The boiler was made of copper about 5™™ thick, and had a total

city of seventy litres. The reservoir B, forming the artificial

•sphere, was also of copper i^mm thick, and contained about
280 litres. The manometer destined to measure the pressure of

.rtificial atmosphere, and thus of the vapour in the boiler,
-istcd of a tube, or rather a series of tubes placed vertically
over one another, and attached to the walls of the building in
the vicinity of which the experiments were performed, and con-
tinued along a strong pole or mast firmly secured to the top of
the wall. This system of tubes was open above, and contained
the column of mercury which measured the tension in B. Its
total height was twenty-four metres, and it was accordingly able
to measure a pressure of thirty atmospheres.

The experiments were conducted as follows. The water in
the boiler having been raised nearly to its boiling point, the air in
the reservoir B was compressed until it had reached the pressure
under which it was desired to make the experiment. A column
<>f mercury of the corresponding height was next forced up the
manometer from below by means of a force-pump, and connexion
was then made between the manometer and the reservoir. IM«
while the temperature of the water in A was rising, and continued
to increase until it reached its boiling point under the pi
which it was exposed. It was then kept in a state of ebullition
for at least half an hour, and no observation was made until
it was | 1 that the mercurial thermometers conne.

with the boiler were perfectly stationary. The temperatures in-
dicated by these thermometers were then observed, and also the
indications of an air thermometer, which, to insure greater accu-

.-, was employed in addition t<> the ti-nn.T. At tin- -
time the dill'ereiice of level of the mercury in the branches OJ
man vas noted. M. Kegnault's experiment- with this ap-

led to a pressure of about i .-lit atmnspl.

id ing to a temperature of23O°.56, menHiied on the air
thermomet. r. F,,r the result? of the j,

. \ i.

/ Sr. A v<i>t' '• ' ; iff <>/i f/i<>

airy. — S'lL-nor Ava^adro ha- |>ul>li.-hed

1 84

EXPERIMENTAL RESEARCHES ON

[BOOK i.

in the Memoirs of the Academy of Turin* a paper on the
elastic force of the vapour of mercury. He has employed in
his investigations the principle that the elastic force of a mix-
of air and vapour is equal to the sum of the forces of each,
considered separately, and that, accordingly, if we ascertain by ob-
servation the force of such a mixture at any temperature, and sub-
tract from it the force of the air, calculated from the known laws
of its expansion, we obtain the elastic force of the vapour alone
at the observed temperature. His apparatus consisted of a glass
syphon, whose shorter branch was closed and terminated in a ball,
containing about one-third of its volume of air carefully dried.
The remainder of the ball, as well as the bend of the syphon, was
filled with freshly boiled mercury, which at the ordinary tempera-
ture stood at about the same level in both branches. This apparatus
was immersed in a bath of fixed oil, whose temperature was raised
by means of a charcoal fire placed underneath. Attached to the
open branch of the syphon was a scale divided into millimetres,
which enabled the observer to determine directly the rise of the
mercury in this branch, and hence, by calculating approximately
the corresponding depression in the ball from the relative areas of
the ball and tube, whose diameters were i$mm and 3mm-75, res-
pectively, to ascertain approximately the difference of level, and
therefore the pressure and increased volume of the mixed air and
vapour at any temperature.

The following Table contains the corrected results of his
experiments.

TABLE of the Tension of the Vapour of Mercury from 230° C. to

290° C.

Temperature.

Pressure.

Temperature.

Pressure.

230°

58mm.oi

270°

1 65""". 2 2

240

80 .02

280

207 .59

250

105 .88

290

252 .51

260

133 .62

* Tome xxxvi. p. 215 (1833).

CHAP. II.]

THE DENSITIES OF VAPOURS.

.85

M. Regnault* also made some experiments on the vapour of
mercury at temperatures inferior to the preceding. The following
Table gives his results.

SEHI

IS II.

SERIES III.

nature.

Pressure.

Temperature.

Pressure.

Temperature.

Pressure.

[00.00

23 -57
38 .01

100 .60

omm.ooo
o .068
o .098
o -555

o°.oo

25-39
49.15

72 .74

100 .11

omm.ooo
o .034
o .087
o .183
o ,407

I00°.6
146.3

I77 .9
200 .5

3 '•$

10 .72

22 .01

" Series I. and II. differ notably," remarks M. Regnault, " when
we compare the relative values which they give for the elastic
forces of mercurial vapour; still the absolute differences which we
observe between these forces are really very small, and of the
order of the errors of observation. The preceding experiments
are, however, sufficient to show that the tension of the vapour of
mercury at 100° is about omm.5, and that at 50° it scarcely reaches
omm .1." "In Series III. the observations evidently became er-
roneous on approaching the temperature of 200°, owing to a
partial distillation of the mercury. The results, accordingly,
can only be regarded as approximations."

SECT. V. — EXPERIMENTAL RESEARCHES ON THE DENSITIES OF
VAPOURS.

'/'/teoretic Determination of Density of Vapour*
Gay-Lu880C8 IMW of Volutn .<. When in tin- form of gases and
vapours bodies reach, as it were, the very limit of material •

lind tin-ill under the dominion of a force, the t
liich is to constrain them t«> follow in their compression the
law of IJoyle and Mariotte, an<l in their expansion by heat that
1 ilton an ,-ac. 'I r physic:

•itnt. t.-iiic x\i p. 502.
2 B

I 86

EXPERIMENTAL RESEARCHES ON

[BOOK i.

pointed out that under the same circumstances the law of chemi-
cal combination assumes a remarkable simplicity of form, for lie
has shown that gases and vapours not only combine according to
definite proportions by weight or volume, as solids and liquids
do, but that the volumes in which they combine always bear to
one another a ratio expressed by some simple whole number; and
further that the volume of the compound bears an equally simple
ratio to those of the component gases.

This discovery of M. Gay-Lussac's of what is commonly called
the law of volumes has been since so amply confirmed by subse-
quent experimenters, as to be regarded one of the best established
laws in physics. The following examples, taken from Turner's
Chemistry,* will serve as illustrations of it.

Volumes of Elements.

Volumes of resulting Compounds.

100 nitrogen + 300 hydrogen yield
50 oxygen + 100 hydrogen ,
50 oxygen + 100 nitrogen
100 sulphur + 600 hydrogen
100 sulphur + 600 oxygen
loo chlorine + 100 hydrogen
100 iodine +100 hydrogen
100 bromine + 100 hydrogen
100 cyanogen + 100 hydrogen
100 oxygen -f 100 nitrogen

200 ammonia.
100 water.
100 protoxide of nitrogen.
600 hydrosulphuric acid.
600 sulphurous acid.
200 hydrochloric acid.
200 hydriodic acid.
200 hydrobromic acid.
200 hydrocyanic acid.
200 binoxide of nitrogen.

When we know the densities and volumes of the elements of
a compound, and the volume of the latter, we can readily deter-
mine its density, from the principle that the weight of the com-
pound is equal to the sum of the weights of the components.
Thus let n, ri, n, &c., d, d, d", &c. represent the volumes and
densities of the elements of a compound ; N, D the volume and
density of the compound itself; the weights of the elements will
be ndy rid, ri'd", &c., and the weight of the compound ND ; and
consequently we have nd + rid + n"d", &c. = ND ; and therefore,

~

nd+ rid + ri'd", &c.

* Turner's Chemistry, H^hth edition, p. 161.

CHAP. II.] THE DENSITIES OF VAPOURS. 187

Now in the case of gases and vapours the quantities ?i, riy n",
V. may all be expressed by simple whole numbers i, 2, 3 ;
hence, if we know the volumes and densities of the elements of a
compound, and have an approximate experimental value for the
density of the latter, we can determine its exact value, since we
know in this case the exact value of JV, which by the preceding
law must be the whole number which gives a value for D nearest
to the experimental one.

Thus we know by analysis that two volumes of hydrogen +
one of oxygen form water, and that the density of the former
gas, as referred to air at o° and 760™™, is 0.06926, and that of the
latter 1.10563, while the density of aqueous vapour, as determined
by direct experiment, is about 0.623. ^n ^is case> therefore, we
, approximately,

2 x 0.06026 + 1.00563

_J> 4-i = 0.623;

N

and accordingly N must equal 2, and the exact value of />,
the density of aqueous vapour, is 0.62207. The density here
spoken of is, as will have suggested itself to the student, the ab-
: density of a vapour, that is (no), its density, as referred to
air at the same temperature and pressure.

In the same way, knowing the volume and density of a binary
compound and of one of its components, we can determine the
exact density of the other component from its approximate value

mined by experin.

From what has been said of the unequal expansion of gases
by heat, when the pressures to which they are submitted are at
all ronsidcniMe, it follows that, under these circumstances, their
volume- will not pi-e.-.-rvo a constant ratio when they un«:-

- of t.-inpeiature. I lence we may expect to i'm.l in
the law (»f volumes the san; fa " limit law," which

<• other laws of gases which we have notio
127. M. Gay-LuMoca Metltod of deter / ;y Experiment

! . — The lir-t nirtho.l . ,f determining cxpe-

ntally tl y of vapours is (It M -sac. It

• volume occupied by a known weight
when eonv< , vapour, at :i -.turc

188 > -XI -1 RIMKNTAL RESEARCHES ON [BOOK I.

and pressure. The apparatus which he employed for this pur-
pose was constructed as follows. A graduated glass jar (Fig. 65),
filled with freshly boiled mercury, was inverted in a metal cis-
tern, MN, containing a quantity of the same liquid, and placed over
a furnace,/. The upper edge of this cistern was ground plane, to
admit of its being accurately levelled, and supported a frame, RS,
to which was attached at right angles a graduated rule, PQ. The
lower point of this rule was brought to coincide with the surface
of the mercury in the cistern, and a telescope of short focus moved
along the upper part, by means of which the level of the mercury
in the jar could be observed, and thus its height above that in
the cistern measured. The jar AB was surrounded by a cylindrical
vessel, cc, containing water or some other fluid, whose point of
ebullition was generally higher than that of the liquid under con-
sideration.

The manner of using this apparatus was as follows. A small
bubble of thin glass, m, filled with a known weight of the liquid
whose vapour was to be examined, and sealed at both ends, was
introduced into the jar AB. In consequence of its superior light-
ness it rose through the mercury, and floated on its upper sur-
face. The furnace being then lighted, the apparatus became
gradually heated, and the glass bubble being burst by the expan-
sion of the fluid which it contained, the vapour which was imme-
diately formed depressed by its tension the level of the mercury
in the jar. When the fluid in the vessel cc was raised to its
boiling point, the elastic force of the vapour in AB was measured ; if
this was found inferior to the maximum force of vapour at the
existing temperature, it was certain that all the fluid had been
converted into vapour ; but if the force was equal to the maxi-
mum, there was no evidence that this had taken place. In
this latter case, therefore, it was necessary to repeat the experi-
ment with a bubble containing a smaller quantity of fluid. When
it was found that all the fluid introduced into the jar hud been
vaporized, the volume which it occupied was observed, and also
its elastic force and temperature, and from these data, and its
known weight, its absolute density was easily computed.

For let v represent the volume at o° of one division of the
jar, k the coefficient of cubical expansion of its material for i° C.,

CHAP. II.] THE DENSITIES OF VAPOURS. 189

T the temperature of the apparatus as given by the thermometer
in cc, and n the number of divisions of the jar occupied by the
vapour; then the volume of vapour equals nv (i + kT), and w
being its weight, the weight of the unit of volume of vapour,
under the circumstances of the experiment, equals

nr(i -IcT)

If // represents the height of the barometer at the time of the
experiment, and h the difference of the heights of the mercury in
the jar and in the cistern, these heights being reduced to their
equivalents at o°, the elastic force of the vapour equals H-h.
Now if W represent the weight of the unit of volume of dry air
at o° and 76omm, its weight at T° and //- h is equal to

760 'i

and consequently the absolute density of the vapour, that is (i 10),
the ratio of the weight of a given volume of the vapour to the
weight of the same volume of dry air at the same temperature
and elastic force, is given by the expression,

_ w 760 I -1- aT .

= i^w- ir^h'TTkT

In an experiment made by M. Gay-Lussac on the density of
•us vapour, the following results were obtained.

The weight of the glass vessel empty was 0^.791
Its weight filled with water was . . . i .391

Tl • equalled ....... osr.6oo

faloe Of 9 WM 0^.00499316, PI • -quailed 220, T= 100°,

and assuming k = o. oooo2( /') = im. 10137, and ti

fore w -4- nv (i + kT), th ir, =

of.5473;

Again, the height of the 1 15° was 755mm.j, con-

• ntly // -5 .;""". 4 ; t! "f the in .1 the jar ,

Ntrrn was 52"'™ at 100°, an-1 therefore h = 5 ilnm.o ;
and thu.^ the rla-tio foiOQ oftl , = 7O2mn'-4-

ipo :KNTAL RK<I:AK( HKS ON [BOOK i.

Assuming W, the weight of the litre of dry air at o° and
76omm, after MM. Biot and Arago, to be equal to 1^.29954, and
1 alue of a to be 0.00375 ; we have,

0^.8730;

.

760 i+aT

consequently D = 0.627.

Moreover, as the weight of iut of aqueous vapour at 100° and
702min.4 equalled 0^.5473, assuming Mariotte's law to hold true,
its weight at 100° and 760""" would be 0^.5925 ; and the weight
of im of water at its maximum density being 1000 grammes, it
follows, from the preceding experiment, that the density of aqueous
vapour at 100° and 760™°', as referred to water at 4°, = 0.0005925,
and consequently the volume occupied by i&r of vapour at 100°
and 760"™ is to that occupied by igr of water at 4°, as 1688: i,
or, in round numbers, as 1700: i.

128. Method of M. Despretz. — It is obviously essential to the
accuracy of the preceding method that the whole of the liquid
should be converted into vapour, and as there is no means of as-
certaining whether this condition has been complied with, except
by so regulating the experiment that the elastic force at the time
of observation is inferior to that due to the temperature, it follows
that this method is inapplicable to the determination of the den-
sity of vapour, when this latter possesses the maximum value due
to the temperature. M. Gay-Lussac, therefore, was obliged to
compute the latter, namely, the maximum density, or the density
corresponding to the maximum elastic force, from the density at
an inferior force, by means of Mariotte's law.

In order to remedy this defect, and at the same time to exa-
mine whether Mariotte's law is really applicable to vapours,
M. Despretz employed the following apparatus for the determina-
tion of their densities.*

This apparatus consisted of a barometer tube, AB (Fig. 66), of
wider bore than usual, closed with a stop-cock, r. The tube being
filled with mercury and inverted in a cistern, a small quantity of
the liquid whose vapour was to be examined was introduced into

* Aunales de Chimieet de Physique, tome xxi. p. 143.

(HAP. II."

THK M:\SITIES OF VAr<

191

the vacuum. A glass balloon, E, also furnished with a. stop-cock, ?•',
and exhausted of air, was then screwed on the top of the baro-

r tube, and, the stop-cocks being opened, the balloon was
filled with vapour. The stop-cocks were then closed, and the
balloon being removed its weight was determined, and, the weight
of the empty balloon and its capacity having been previously as-

ined, the weight and volume of vapour were known. If
tlu-iv was liquid in excess, the elastic force of the vapour and its
density were at their maximum for the temperature of the sur-
rounding medium ; but if there was a deficiency of liquid in pro-
portion to the volume of the barometric chamber and balloon,
the density was inferior to the maximum. The elastic force was
given by the height of the mercurial column in the tube, com-
pared with that of a barometer, CD, immersed in the same cistern.
The temperature was always that of the air at the time of the ex-
periment.

From the weights of vapour which filled the balloon at dif-
ferent temperatures and pressures, M. Despretz calculated the
weights of a constant volume at a constant temperature, under
the diffe rent observed pressures; and on comparing these we:
and pressures he arrived at the conclusion, that in the liquids
which he examined, namely, sulphuret of carbon, ether, and
water, " the densities of vapours reduced by calculation to a fixed
temperature are proportional to the corresponding elastic forces,"
that is, that Mari«. tie's law is applicable to vapours, as it is to
permanent gases.

The following Table exhibits a view of his results:

Vapours.

t . If. 1C.

/•

w

7

Imret of car-

i?°.87 8«M87 *•"/>??

Om. l«j<;i

A J.J.7

lo,
•to,
;to,
Ditto,

I4. 194 5 ..:

15 .26 3 .285 3 .470

3 -°53 3
15 -34 2 -773 * -932
1 2 .04 4 .067 c .230

o .1272
o .0797

0 .C

o .0686
o .1270

TJ'T/

IJ

43-53

42-74

41.

.

ii -43 3 -»y7 3

IQ .71 O .1 34. O . IJ.2

o .0820
o .0137

41.02

10.36

Di

44 o .102 o .ioS

0 .0100

1 0.80

lp2 EXPERIMENTAL RESEARCHES ON [BOOK I.

In the preceding table t is the temperature of the vapour, w
tho weight of vapour filling the balloon at that temperature, w'
the weight of vapour at o°, calculated from Gay-Lussac's law of
expansion, which would fill the balloon at 15°, when its capa-
city equalled 9lit.3 746, and finally / the observed elastic force.*

The last column gives the ratio -7-, which should be constant for

the same vapour, on the supposition that Mariotte's law applies
to it, and in the case of different vapours is proportional to their
absolute densities.

129. Method of M. Dumas. — Neither of the preceding me-
thods is applicable to vapours which act chemically upon mercury,
or require for their formation a temperature much higher than
that of boiling water. M. Despretz's method, indeed, is only
applicable at temperatures which do not differ much from that
of the surrounding medium. For vapours, accordingly, which
fall under either of the preceding classes, we must employ the
method of M. Dumas,f which is of very extensive application,
and susceptible of considerable accuracy. This method consists
in ascertaining the weight of vapour filling a balloon of known
capacity, at a temperature superior by 20° or 30° to the boiling
point of the liquid, and under the atmospheric pressure. M. Du-
mas' method of operating was as follows:

A balloon of glass (Fig. 67), whose neck was drawn tout to a
capillary termination, was filled with perfectly dry air, and
weighed, the temperature and barometric pressure at the time
being noted. A small quantity of liquid was then introduced
into the balloon, which was placed in the bath, by means of
which its temperature was to be raised. This bath varied in
M. Dumas' experiments according to the temperature required.
If this temperature did not exceed 150° C., he employed di-
luted sulphuric acid, contained in a cylinder of glass enveloping
the balloon, and placed in a cistern of mercury, as in M. Gay-
Lussac's method. If the temperature was required to reach
200°, he made use of concentrated sulphuric acid, contained

* In making this calculation M. Despretz 0.003 75> according to M. Gay-Lussac.

!tli(M..rtrnif-nt of cubical expansion f Annalcs de Chimie et de Physique

<.f tflaw to be o.ooo 026 8, after MM. La- (2m(i Serif), toiw xxiii. p. 342 (1826).

;iml L'iplarc ; ami that of vapour,

CHAP. II.] THE DENSITIES OF VAPOURS. 193

in a glass vessel set in a sand bath, to guard against accidents
which might arise from fracture ofthcvc- ing the acid.

And for temperatures superior to 200° he used a bath of D'Arcet's
fusible metal.

For these different forms of bath M. Mitseherlich has since
substituted, with great advantage, one of chloride of zinc.

When the temperature of the balloon was raised to within a
few degrees of the boiling point of the liquid which it contained,
the vapour of the latter began to issue from the orifice, and dis-
place the air, and as the temperature increased the vapour
projected in a strong jet, and with a loud, whistling noise, which
subsided when the liquid was all vaporised, and thus gave evi-
dence that the balloon was then filled merely with vapour. The
temperature of the bath was then considerably raised, and kept
stationary for some time, at the expiration of which the end of
the capillary tube was sealed with a blow-pipe, the temperature
and barometric pressure being noted. Before sealing the vessel
it was necessary to observe if any condensed liquid was lodged
in the tube, and if so to vaporise it by passing a live coal along
The balloon was now removed from the bath, carefully dried,
and allowed to acquire the temperature of the surrounding me-
diuin, when it was again weighed, observing the atmospheric

:re and prosure.

It now only remained to ascertain the volume of air which
i al"iii: with the vapour in the balloon, and also the vo-
lume of the latter. Ther-e volumes M. Dumas obtained bv o]
the capillary termination of the tube under water, the latter
B balloon and condensed ili<- vapour, while
;iir remained in a bubble above the water at the top of the
balloon. This air was then o.llectrd and measured, its teiin
UK! pre- :<r observed.*

balloon was m-.\t 1 quite full of water, and all the

lined which ' .uisite for the ealcula-

'luine «i|' the ball. M, M ; ii. «.f tin- volume ..fair
lining with the vapour: and i

rcand prcMoreoft i w.-iuh..l. HM with th

rinth.-l.nl! MTVtd, '•

it ini^ht have boon ; i full.

2 C

I 94 1 XI'KKIMKNTAI. It KSKARCHES ON [BOOK I.

130. Formitiv. of Calculation applicable to M. Dumas MetlnnL
— M. Dumas' method of calculation was as follows. Let w be
the weight of the balloon filled with dry air, w its weight full of

mixture of vapour and air, and IF" its weight full of water, at
the trmpiM-ature t of the surrounding medium. Then the approxi-
mate volume of the balloon, expressed by the weight of water
which it contained, was equal to (W-w) + (W—w) S, if 8 re-
present the ratio of the densities of air and water under the cir-
cumstances of the experiment. For w was in fact the weight of
the glass vessel + the weight of the dry air it contained - the
weight of air displaced by the balloon at the time of the experi-
ment ; and assuming as a first approximation that the weights of
these two volumes of air were equal, we have w = the weight of
the balloon. Further W represented the weight of the balloon
-f the weight ( W) of the water it contained - the weight of
the volume of air it displaced, and if this volume is expressed
by the weight W of water which would occupy it, the weight
of air occupying the same volume will be IF'S, for the weights
of equal volumes of different masses are as their densities ; there-
fore

W = w + W - W'$t or W' = (W- w) + W'S.

Now as 8 is very small, we may put for W, which multiplies it,
the rudely approximate value, W-w (obtained by neglecting
the quantity W"& in the preceding equation), which gives finally

W'= (W-<w) + (W-w}%,

as above.*

Having thus ascertained the volume of the balloon, M. Du-
mas next calculated from it the weight w" of the air it con-
tained, which in fact was equal to W'§\ this being known, he
was able to determine the weight of the mixture of vapour and
air. For the weight (w) of the balloon full of the mixture
equalled the weight of the glass (iv) + the weight of the mixture

' OrMnceJr=(Jfr-tr) + JF£, we have which, if we neglect fc, becomes W =
i - £) = W - w ; therefore W = ( W- to) (i -4- 8) = ( W- w) + ( W-w) S,
{* "' -K! ' >(.- c) ', as in the text.

CHAP, ii.] THK DBB .TOURS. 195

( ll'i) - the weight of air displaced by the balloon («•"); therefore

w = w + H ',
and

IT,

The volume of this mixti* iien corrected for tempera-

ture, pressure, and dilatation of glass, and reduced to o° C., and
o"\~6. The volume of the air remaining in the mixture
also reduced to its value under the same conditions, and corrected,
moreover, for the presence of aqueous vapour ; it was then sub-
tracted from the volume of the mixture, the same operation was
performed on its weight, and there remained, finally, the corrected
values of the weight and volume of pure vapour.

Let FO represent the volume of the balloon at o°.

This volume is thus found. W, the weight of water filling
the balloon at the temperature t, having been ascertained as above,
expressed in grammes, we obtain immediately the weight ( IF"),
which would fill it at 4°, the temperature corresponding to the
maximum density of water. For, taking this latter density as
unity, and representing by A' the density of water at 2°, as given
by Despretz' or Halstrom's tables, pp. 73, 74, we have II : H' ::

H'

i : A, and therefore W" = — 7- Now as 1000 grammes of dis-
tilled water at 4° occupy one litre, the volume of the balloon at

ir ir

t°y or Vt : i1'1:: — r : 1000, and therefore Vt = ;; and -

A loooA

if /.• represent- tin- coefficient of expansion "f i:la>s for i° C.,
I -
— £-, we have, finally,

"'

i ooo A' ' i -t- /•/'

present tin- temperature of the bath when the balloon
:, and // the corrected height of the bar,. meter at the

volume of air remaining io the hal
over water, and sa with aqueous vapour at th«

•I under // : and f th-

vapour at / , BO that // the air a!

:l:cr, let illoon

ip6 uriiKS ON [BOOK i.

full of the mixture of vapour and air, taken when the tempera-
ture of the surrounding medium is t" and the height of the baro-

// ; and -w the weight of the balloon itself.
Then the volume of the balloon at the time of scaling is
i + kT) ; this is also the volume of the mixture of vapour and
at T° and //; at the temperature o° and under the pressure
•j6onim it would be

V(i+kT) H_
i+aT '760'

The volume of air contained in this mixture is equal to v at
the temperature t' and under the pressure H' -/; at o° and *j6omm
it would be

v H'-f
I + at' 760 '

Consequently the volume of vapour alone at o° and 76o"lm is

Vo(i+kT) H v ff-f

I + a T 760 I + at' ' 760 '

and the weight y of the same volume of dry air, under the same
circumstances of temperature and pressure, is

f Vo(i+kT) H v H'-f^ gr

J~ \ (I+aT) 760 i+af '760 J I

tlie volumes V and v being expressed in parts of a litre.

It now remains to determine the weight of the vapour alone.

The weight of the mixture of vapour and air is, as we have

i, = w - w + the weight of air displaced by the balloon at the
tune of weighing. The volume of the balloon being then

i + kt")9 the weight of the air displaced by it is

-quently the weight of the mixture of vapour and air is

0(i +&") H"

ii_J._.

CHAP. II.] TIIK DENSITIES OF VAPOURS. 197

The volume of remaining air at t and (// /) is <•, conse-
quently its weight is

therefore the weight |3 of vapour alone is

rFo(i+*Q //"

Q = (w -«•) + (1-293) I ~ ~^- • —
\ l+af 760

And the absolute density, Z>, of the vapour is given by the ex-
pression

z>-§.

7

These formulae may easily be reduced to English measures,
in which the weights are expressed in grains and the volumes in
cubic inches. For let W" be the weight of water at 62° F., which

W

would fill the balloon, we have W" = — r A", if A" represents

the density of water at 62°; and as (p. 104) 252.722 grains of dis-
tilled water at 62° occupy one cubic inch, we have

*-— •£

252.722 A
and

252.722 ' A' " i -f k(t - 32) *

/:' being the coefficient of expansion of glass for i° Falir.

.iicing the volumes of vapour and air to 32° Fain

30', the exjiie.v-'mn for y becomes

i «</' 32°) "30 " i+a'(*'-32)~3o

of one cul>ic inch (.fair at 32° and 30' is «-«jual
to 0^.32776,* and that for /3

// V II

— J

/ :t,l-»--32; V M

— TT - . - J- \.

\ n ( ' I M / ^2) 30 J

^117.

I98 I Xl'KH I MKNTAL RESEARCHES ON [BOOK I.

\\ .• give as examples the results obtained by M. Dumas in
the case of the vapour of iodine, and of protochloride of arsenic.

Iodine.

107^.532, balloon full of dry air at 24° and om.y57, . . ir.
1 10 .025, balloon full of vapour and air at 185° and om-757, = w.

664 .550, balloon full of water at 22°, =11'.

out.o66, air remaining in vapour, measured over water

at 22°, and under the pressure om.757.
Hence weight of litre of vapour of iodine = 1 1^.323, and
absolute density = 8.716.

Protochloride of Arsenic.

97^.432, balloon full of dry air at 25° and om-758, . . = ic.
99 .420, balloon full of vapour (pure) at 175° and om.758, = w.

638 .740, balloon full of water at 23°, = W.

Hence weight of litre of vapour = 8^.1852, and absolute
density = 6.3006.

The composition of this vapour* being i volume vapour of
arsenic -f 6 volumes of chlorine = 4 volumes of vapour, and the
densities of vapour of arsenic and of chlorine being 10.37 and
2.44 respectively, the density of the vapour of the protochloride,
according to the law of volumes, is given by the expression,

10.37 +6 x 2-44

- = 6.251.

4

131. M . Regnautts Method of determining the Density ofaquco n&
Vapour^ I. in vacuo, (a) at the Temperature of boiling Water y and
under feeble Pressures. — We have seen that, on the supposition
of the applicability of Mariotte and Gay-Lussac's laws, the density
of a vapour, referred to any fixed standard, may be calculated
from its absolute density, and further, that, on the same supposi-
tion, this latter quantity has a constant value for the same va-
pour. And as it is of the utmost importance in hygrometrical
researches to know to what extent those laws may be held to
apply, without sensible error, in the case of aqueous vapour,

" Regnault, Our.* <!<• L'liiiuic, tonic i. p. 309.

CHAP. II.] THE DENSITIES OF VAPOURS. Jpp

M. Rcgnault has made two series of experiments with this object.
Jn the /u-*t he lias inv ! the density of aqueous vapour in

'•>, (a) at the temperature of boiling water and under feeble

-arcs, not exceeding half an atmosphere, and also (/3) at tcm-
piTatun -s extending from that of the surrounding medium to
about 40° C. above it, and under di tie-rent pressures. In the

//'/ lie has examined the density of vapour in azr, at its maxi-
mum for the temperature between the limits of o° and 25° C.

In the conduct of these experiments M. Reimault has intro-
duced several important modifications and improvements of pre-
vious methods, which we purpose briefly to bring before the
notice of the student in the following pages.

(a). To ascertain the density of aqueous vapour in r<into, at
the temperature of boiling water, and under feeble pressures,
M. Regnault made use of the following apparatus.

A (Fig. 68) represents a glass balloon about ten litres in ca-
pacity, to the neck of which is attached* a brass mounting fur-
nished with a cock, r. Into this balloon a small quantity of water
is introduced, and connexion is made with an air-pump, a tube
containing coarsely powdered pumice stone and concentrated
sulphuric acid being interposed to prevent the aqueous vapour
penetrating ini" tin- pump. Tho vacuum is maintained for a
Considerable time, and the vapour of water which is perpetually
formed iii the balloon, eventually expels all the air from it. when

cock /• is closed. The balloon is then place* 1 in a v«
BCDK, of Lralvani/.ed sheet iron, so that the cork /• is opposite the

'The method of < i nting this mount- and ti.. •;„> balloon: t,> p-

ith tin- in -ck of ili- l,:ill....u i- iv|'iv- any pa-in- into tin- ' Y. tli,-

aented in Fig. 69. The momtinf OOMfati upper edge, inn. i- »-ar. fully -muii:-!

Of two pieces, abed, rfyt,. nlii.-li. cm L.-in^ tin- iiiMimtiii-. Tl,i> .viu.nt ,,mVk!'

screwed to^ POM between th.-m dens, especially if the balloon i* w p*-

* piece of hemp packing lying in the an- heated in ih>- vaj.. -nr • i Ix-ilii

nular spa.-.- «.». This packing is saturate 1 fnrn.H ;l p, Ti. it l,,w

uitli a (.in. ut fonned of equal parts of mi- butalwiathi^li t nM inures, and possesses

niiim aiul r.-niM-. w hi. h ar-- rul.l.«.,l (.,-,-- tli.-'a.Miii..nal advantage • • lial.l.'

ili.-r \Mth linseed oil, no as to f.-nn a tliick to crack in consequence of >n.|.i.-n .-hanges
paste. When the pack

a i»orti..n ..f tli.- OSBM I "'• Serie), ton

int<> tho space bet^>

200 EXPERIMENTAL RESEARCHES ON [BOOK I.

tubular opening T. This vessel contains a quantity of water,
two diviinrtres deep, and is heated over a furnace. The cxtre-
initv «>f the tube be is connected with the brass tube cd, which is
itself soldered to a flexible lead tube, de, constituting part of the
mounting N of a large jar F. This jar is maintained at the tem-
perature of the surrounding medium, and a small lead tube, £,
puts it in communication with an air-pump, and the barometric
manometer represented in Fig. 70.*

A partial vacuum having been made in the jar F, the cock
r is opened when the water is boiling briskly in the vessel BCDE.
The vapour passes over, and is distilled in F. At the expiration
of about an hour the force of the vapour is observed by means of
the manometer, and the cock r is closed.

The tube be is now detached from cd, and carefully dried, and
the balloon removed from BCDE and weighed, after having been
allowed to remain for twenty-four hours suspended from the scale
of the balance.

After its weight has been ascertained the balloon is again
placed in the vessel BCDE, and in connexion with the jar F. The
water is brought up to the boiling point, and a very advanced
vacuum made in F. The cock r being opened, the greater part
of the vapour is condensed in the jar, and there only remains a
quantity which equilibrates the pressure in F. This latter force
is carefully measured after the equilibrium is established, and the
cock r is then closed. The balloon is again weighed as before.

If these weights are determined by the ordinary methods, al-
lowance should be made for any change which may have taken

* This manometer consists of a perfect to do when frequently repeated, by forcing

liaruineter, AH, and a barometer tube, CD, minute quantities of air through the mer-

kbore, I H'th secured to the same board, ctirial column. When in use the mercury

and standing in the same cistern. When this is brought to the level of the lower point

in>trmi]i-nt is not in use, mercury is allowed of the screw v, and the heights of the co-

to flow out of the cistern through the cock lumns in the two tubes above the upper point

R, until the level falls below the top of the of the screw being observed by a kathcto-

ion mn, by which means all commu- meter, these heights, increased by the height

niration is cut ofl' In twci n tlio two tubes. of the screw, which has been previously as-

Thi- i> fi.nii'1 iit-c.-><ary in order to prevent cerfaim-d, give the true heights of the co-

I'lilrn (.-filiations in the open tube af- lumns in the
•he vanillin in AH. a- tlu-y arc apt

CHAP. II.] THE DENSITIES OF VAPOURS. 2OI

place, during the interval between the weighings, in the weight of
the volume of air displaced by the balloon, and also in the small
amount of moisture which is always condensed on the surface
of glass vessels, apparently by some kind of molecular action.
This latter quantity, which is, no doubt, in ordinary circum-
stances, very minute, we have no means of estimating with ac-
curacy ; the former might be calculated if it depended merely on
changes of temperature and pressure, and on variations of the
hygrometric state of the atmosphere, but there appears reason to
believe that, where the observations are separated by an interval
of some hours, the weight of a given volume of atmospheric air
is also affected, though to a very slight extent, by changes which
take place in its constitution.

In order to obviate, then, the necessity of those corrections,
and the consequent liability to error, M. Regnault followed, in
these experiments, the same method of weighing which he had
adopted in his experiments on the densities of gases. The pecu-
liarity of this method consists in equilibrating the balloon, not
with weights, as in the usual way, but with another balloon full
of air, hermetically sealed, constructed of the same kind of glass
as the former, and having exactly the same external capacity.
Any alteration produced, then, in the weight of the gas contained
in the balloon A, was exactly represented by the counterpoise ne-
cessary to restore equilibrium, — neglecting as quite insensible the
weight of the air displaced by the counterpoise itself, — for the
volume of air displaced by the balloon, and the moisture con-
densed on its surface, were accurately equilibrated at any instant
by the similar quantities in the case of the other balloon, and the

lit <>f the balloon itself, and of its mounting, of course
mained unaltered*

This second balloon, B, was prepared as follows. Ha
filled the balloon A with water, M. Regnault writhed it first in
water and then in air, in this way he ascertained the weight of
water which it displaced. He tin d another balloon of

-amc kind of glass, which displaced as nearly as possible the
unity of water, and accordingly had nearly :

I the neck "I' this balloon he , d a

202 EXPERIMENTAL RESEARCHES ON [BOOK

I cap. and if the displacement of this cap, added to that of the

balloon itself, was still inferior to the displacement of A, he se-

1 a piece of glass tube, sealed at both ends, whose displace-

ment equalled the difference. This he succeeded in doing with-

out difficulty after a few trials.

If the balloon B, with its mounting, was lighter than A, M.
Regnault introduced a little mercury into it before sealing, so
that the addition of a small weight was sufficient to render the
equilibrium perfect.

When taking the weights the balloons were attached by hooks
to the scales of an accurate balance, so that they floated in ex-
actly the same stratum of air. They were, moreover, enclosed
in a case which protected them from local currents, and also from
any effects which might be produced by the presence of the ex-
perimenter.

As a proof of the accuracy of this method, M. Regnault men-
tions that two balloons, suspended as described above, remained
in perfect equilibrium for upwards of fifteen days, although in
the interval the temperature had changed from o° to 17° C., and
the pressure from 74imm to 771"™.

To return to our experiment, let w be the weight of the coun-
terpoise necessary to restore equilibrium after the partial exhaus-
tion of the balloon A.

This is evidently the weight of the quantity of vapour which
would fill the balloon at the temperature T of boiling water, and
under the pressure 7i, equal to the difference of the pressures ob-
served in the two cases.

Let W be the weight of dry air which fills the balloon at o°
and 760™™. This weight was determined by direct experiment.
The weight of air at T° and h, filling the balloon at T°, is evi-
dently

.

760 1+aT

where a is the coefficient of expansion of dry air, and k that of
the glass balloon for i° C. Therefore the absolute density of
aqueous vapour under the circumstances of the experiment, being

CHAP. II.]

THE DENSITIES OF VAPOURS.

203

equal to the former of those weights (w) divided by the latter,
is represented by the expression,

w i + a T 760

The following Table contains the results of four experiments
made in this way :

Number of
Experiment

W.

w.

T.

/i.

D.

I

2

i2gr-9937

2^.959

2 .802

99°-9I

on .14.

378-.72

2C7 .CI

.62311
.62377

2

I .26l

QQ .6?

161 .32

.62292

2 .606

Q9 .78

34C .28

.62229

The near agreement of the numbers in the last column with
one another and with the theoretic density, shows that Mariotte's
and Gay-Lussac's laws are applicable within the limits of the
preceding experiments; for, as was remarked (112), the absolute

-ity of a, vapour is not constant, except on the supposition of
the applicability of those laws.

On applying the same method, however, to the determination
of the density of aqueous vapour at the temperature of boiling
water, and under pressures which approach more nearly to "j6omm,
values were obtained for D, which are sensibly larger than the
pr.T.'ding, proving, as might have been expected from the aim-
logy of permanent gases, that the density increases more rapidly
than the elastic force, when the vapour is near its point of maxi-
mum density for the temperature, and consequently near its point
uf liquefaction.

The preceding method is inapplicable, except at the tempera-
ture of boiling water; it fails also in giving accurate results at
very feeble pressures, as the least error in the weights prod.

ones in the numerical value for the den-it v. In
lore, correct values for the density at tem-
peratures approaching more and m<>iv nearly to that of -atura-
M I! uuilt had 1600 method.

204 EXPERIMENTAL RESEARCHES ON [BOOK I.

132. Method of determining the Density of aqueous vapour in vacuo
(j3) within a limited Range of Temperature on either Side of that of the
surrounding Medium, and at Pressures gradually diminishing from the
Maximum. — ()3). The capacity of a large balloon of glass is accu-
rately determined by weighing it when full of distilled water at a
known temperature. Into this balloon is introduced a small glass
bubble, hermetically sealed, and full of water, whose weight is care-
fully ascertained. The balloon is connected with an air-pump and
manometer, as in the last method, and both it and the manometer
are enclosed in vessels of water, in the manner represented in
Fig. 38, and the usual precautions are taken to insure unifor-
mity of temperature through the apparatus. The interior of
the balloon is next carefully dried, and, after as perfect a va-
cuum as possible has been made in it, the pressure of the air re-
maining is observed. The glass bubble is then broken by means
of some live coals, and the temperature of the water surrounding
the balloon raised above the point of saturation of the vapour.
This will be known to be the case when the elastic force, as given
by the manometer, diminished by that due to the remaining air,
is inferior to the maximum force of aqueous vapour at the exist-
ing temperature.

If V, expressed in cubic centimetres, represents the volume at
o° of the balloon and part of the manometer tube occupied by
the vapour in these experiments, this volume at t equals V(i + /•£),
k being the coefficient of glass for i° C., and w being the weight
of water introduced into the balloon, which we will suppose at
the temperature t to be all converted into vapour, we have for
the weight of icc of the vapour at t° and the observed pressure/,
the expression

w
V(i+kt)'

The weight of icc of dry air at o° and 760 M. Regnault assumed,
after MM. Biot and Arago, to be 0^.0012995, consequently its
weight at t and /equals

osr.oo 1 29 95 . -~- ;

3 I + at 760

CHAP. II.]

THE DENSITIES OF VAPOURS.

205

and the absolute density of the vapour, in terms of the data of
the preceding experiment, is given by the expression,

~ _ w i + at 760

1^(0.0012995) ' i -f kt * /

The following Table gives a view of the results of some expe-
riments made by this method, in which

V- p6i2cc.4, and w = 0^.308.

No. of
Experi-

t.

*

*

Ft

D.

I

i c°.o6

I2mra.8l

i2mm.75

I.OOO

2

j '^

21 Q7

21 .8c

I.OOO

2C Q!

•y /

2 C ,OC

wj

2J. Qf

I.OOO

4

30.82

32 .14

• T *y *
32 -H

I.OOO

0.646 93

5

31 -23

32 .66

33 -86

0.964

0.638 49

6

31 -54

33 -24

34 -46

0.964

0.627 86

7

32 -37

33 -49

3« -47

0.870

0.624 99

8

37 -05

34 -'9

46 .82

o-733

0.621 40

9

41 .51

34 -65

59 -51

0.582

0.621 95

10

41 .88

34 -61

60 .68

0.570

0.623 33

I I

45.78

35 -22

74 -33

0.474

0.620 03

12

48.38

35 48

84 .84

0.418

0.620 46

'3

55-4'

36 .23

119 .84

0.302

0.620 78

Ft denotes the maximum tension of vapour due to the tempe-
rature, t uken from M.Regnault's tables; '-p-, the ratio of the elastic

force observed to the maximum force at the temperature, is ge-
nerally cullnl tin1 / "/'.«/////•<'/'

In experiments i, 2, 3, liquid was in excess, and accordingly

KM had its maximum value; in tin- remaining rx["'-

rim-'ii:- tin; value of this force was inlcrior to the maximum,

liquid, therefore, was all converted into vapour, and the data
.•alculation of the density.

Th«- exjM-iiments from 8 to 13 give for this density numbers
sensibly e«|ual to one another and to the thcon-tie density, thus

Mi.-hin;: within their limits the appliealulit \ M i.-tte and

Qty-Lussuc's laws. I »ut the ezperimenti i'r..m .} t« 7. which

||« saturation

206 EXPERIMENTAL RESEARCHES ON [BOOK I.

of the space, give for the density values much greater than the
preceding, and constantly increasing with the fraction of satura-
tion.

" From this we may conclude," says M. Regnault, " that the
density of aqueous vapour in vacuo and under feeble pressures may
be calculated according to Mariotte's law, provided that the fraction
of saturation does not exceed 0.8; but that this density is notably
greater when we approximate more nearly to the state of satu-
ration.

" This latter circumstance may be owing to one or both of two
causes ; either aqueous vapour really suffers an anomalous con-
densation on approaching its point of saturation, or a portion of
the vapour remains condensed on the surface of the glass, and
does not assume the aeriform state until the mass of vapour is at
some distance from the point of saturation. The daily experience
of our laboratories proves the hygroscopic attraction of glass ; this
substance holds water condensed on its surface, even when it has
remained a long time in air far from its point of saturation, so
that we cannot doubt but that the hygroscopic affinity of glass
has some influence on the phenomenon in question, though it is
difficult to decide whether it is its sole cause. If we were to de-
termine the density of aqueous vapour near its point of satura-
tion, in balloons of different materials, or in glass balloons covered
with different kinds of varnish, or in balloons of this material of
very different forms, presenting, accordingly, very different pro-
portions between their surface and capacity, we might, perhaps,
arrive at an approximate estimate of the influence exerted in the
present case by the nature of the surface. But it would be diffi-
cult to get rid of the superficial condensation completely and with
certainty."

133. II. M. Regnault s Method of determining the Density of-
aqueous Vapour in Air, in a State of Saturation. — M. Regnault
describes as follows his method of determining the density of
aqueous vapour in air, at its maximum for various tempera-
tures.

" I have determined the density of aqueous vapour in a state
of saturation in air, by weighing the quantity of moisture which
a known volume of air, when saturated, contains ut different tern-

CHAP. II.] THE DENSITIES OF VAPOURS. 207

peratures. For this purpose I have employed the method of
M. Brunner, which consists in filling with water a vessel of known
capacity, and then, after putting the upper part of this vessel,
which is called an aspirator, in connexion with tubes containing
desiccating substances, in allowing the water to flow out at a
uniform rate through an orifice below. The water thus withdrawn
from the aspirator is replaced by an equal volume of air, which
has been deprived of all its moisture on its passage through the
desiccating tubes. These tubes are weighed before the aspira-
tion has commenced, and after the water has all flowed out of
the aspirator, and the difference of the weights represents the
weight of water contained in a volume of air equal to the capa-
city of the aspirator.

" The aspirator which I employed consists of a cylindrical ves-
sel (Fig. 71) of galvanized sheet iron, terminated by conical ends.
The upper part contains two tubular openings, the one, a, central,
in which is hermetically secured a tube, #', which acts as a Ma-
riotte's tube in rendering the flow of water uniform ; through the
second aperture, Z>, is passed a thermometer, T, whose reservoir
occupies the middle of the vessel. The lower part has a single
tubular aperture, with a graduated cock, R; this cock has a dis-
charge pipe, one decimetre in length, which remains filled with
water after the discharge is completed, and prevents the entrance
of air by the inferior aperture when the aspirator is emptied.

" The Marietta's tube has a cock, r, which serves to stop the

ration of air, and a U-shaped tube filled with sulj >/m;v> pumice,
which is constantly attached to the apparatus; the object of this
tube is to prevent the vapour of the water in the aspirator reach-

the desiccating tubes u and c.

44 To absorb the moi.-tim- <>|' tin- ;iir I <>nly employ two
U-shaped tubes, u andc, om.i8 in height, and filled with sulphuric
pumice in larg'1 illiOed t«> line powder it would

pie.-ent too great a resistance t<> the il«>w ol'thc air, and n
quently the air in the aspirator would not possess the same clastic

•<• as th«- •

Alter having de-crilied >..me experiment- l>y which lie satia-
that these tubes were suflicient to absorb all the
.tained in the air drawn into the aspirator, M . I

208 EXPERIMENTAL RESEARCHES ON [BOOK I.

nault states his reasons for desiring to render this part of the ap-
paratus as small as possible. These reasons are founded on the
uncertainty attached to the weights of vessels of glass of con-
siderable dimensions, determined under different atmospheric con-
ditions, arising from the circumstances to which we alluded in a
previous paragraph. He then proceeds to describe the part of
the apparatus designed to saturate the air with moisture before
its aspiration.

" A vessel of tin, MN, of twenty -five litres in capacity, closed
above, is placed in a large dish full of water ; this vessel has three
tubular apertures. The upper aperture e admits a very sensitive
thermometer, whose reservoir occupies the centre of the vessel ;
in the aperture / is fitted the extremity of the first tube c, so
that this tube may derive the air from the middle of MN ; and
finally, by means of the aperture #, the vessel is put in commu-
nication with the balloon o, filled with wet sponge, which the air
is obliged to traverse before entering the apparatus. To insure
still further the saturation of the air, a cylinder of wove wire was
placed in the interior of the tin vessel; this cylinder was covered
internally and externally with moist linen cloth, which dipped
into the water covering the bottom of the dish. A little opening,
o, in the side of this cylinder, allowed the air to be drawn from
the middle of the vessel, and in the neighbourhood of the reser-
voir of the thermometer.

" This apparatus was arranged in a room whose temperature
varied very little, and no experiment was commenced until some
time after it was put together. The rate of aspiration of the air
within certain limits made no difference in the results of the ex-
periment. Thus in one case the water was drawn off in forty-five
minutes, in another in three hours, but the weight of water col-
lected in the tubes B, c was exactly the same in both experiments.

" Under ordinary circumstances the aspirator was emptied in
ih 15™ or ih 30™. Every five minutes the thermometer in the
tin vessel was read from a distance by means of a small telescope,
and the mean of the observed temperatures was taken as the tem-
perature of the saturated air. These temperatures never varied
above one or two tenths of a degree. When the water ceased
to flow a few minutes were allowed to elapse, to permit the air

CHAP. II.] THK DENSITIES OF VAPOURS. 2Op

in the aspirator to acquire exactly the pressure of the external air;
the cock r was then closed, and the thermometer r, as well as the
barometer, noted.

" To obtain the quantity of water in air saturated at o°, I
made use of the following arrangement. A tin tube (Fig. 72),
om.55 long and om.io in diameter, has in its axis a tube, ab, om.o2
in diameter. This tube is open at its two ends ; a lateral open-

. cd, forms the communication between the tube ab and the
drying tube c. The upper end of the tube ab is closed. The
outer vessel is filled with pounded ice, which escapes when melted
through the cock r.

" When the aspirator is in operation, the exterior air is drawn
through the ice, which reduces it to o° ; it enters the tube ab
through the inferior orifice, and from thence passes into the desic-
cating tubes through the orifice cd.

" Now let

t represent the mean temperature of the saturated air ;

/the maximum elastic force of aqueous vapour at that tempera-
ture;

i the temperature of the aspirator at the end of the experiment ;

/' the elastic force at the temperature t ;

// the barometric height reduced to o° at the end of the expe-
riment;

a the coefficient of dilatation of air for i° C. ;

/ that of sheet iron, assumed to be 0.0000366;
r the volume of the aspirator at o°.

I he volume of the aspirator at t will be V(\ +/•/); this i> the
volume which tin- air drawn through the tuhes had in the u-pi-

rator at th<- oonckiflion of the experiment, Imt it wa> then satu-

1 with vapour of water, whose elastic force was/, ther.
til-- an alone had a pressure equal only to // / . whereat when
in the tin vessel it.- preMUN ITtl // f\ <•»!!- 'juently its volume
in tlu- latter case would have 1

// /

// /'

210 EXPKKIMKXTAI. KKSEARCHK> OH [BOOK I.

luul its temperature been the same as in the aspirator; but as its
temperature in MN was t, its volume there was really

,7 , II -f i + at

41 If we represent by w the weight of a cubic centimetre of air
at o° and 76omm, and by 8 the density of aqueous vapour taken
relatively to that of air, — that is, its absolute density, — then, sup-
posing that aqueous vapour in a state of saturation in air follows
the same law of dilatation and pressure as air, that is, that Gay-
Lussac's and Mariotte's laws are applicable to it under those cir-
cumstances, we shall have for the weight of aqueous vapour
contained in the preceding volume of air, the expression

,T, , H-f i + at « i /
V(i+kt) J . - - .108 - --£-,
H-f i + at I + at 760

or

F(I +kt) -i^ -^ • »s -4--

H-f i + at 760

" Equating this expression to the weights determined by ex-
periment, we should have a series of equations to determine S, by
means of which we might assure ourselves whether this value is
constant for all temperatures.

" I have preferred calculating by means of this formula the
weight of vapour which should be found in the preceding volume
of air, supposing § = 0.622, the theoretic density, and comparing
this weight with that derived from direct experiment. The result
of this comparison is, that all the numbers obtained by calcula-
tion are a little greater than those found by experiment, and this,
sensibly, by the same fraction of the total weight. This fraction
is very small, and amounts to about one-hundredth.

" From this we may conclude that the density of aqueous vapour
in air, in a state of saturation, and under feeble pressures, may be
calculated from Mariotte's law; and that the ratio of the weight of a
volume of this vapour to that of the same volume of air, under the
same circumstances of temperature and pressure, is a little less than
the theoretic density of aqueous vapour.

CHAP. II.] THE DENSITIES OF VAPOURS. 21 I

"It is true," adds M. Reimault, " that we may explain in
another wav this difference between the observed and calculated

Jits of vapour. We may admit that the density of aqueous

vapour, under the preceding circumstances, is the same as that

which we have found in racuo, namely, 0.622, but that the values

of the elastic force, /, employed in the calculation, and which

taken from mv table of the clastic forces invacuo, are a little

large: and this would accord with the result of my experi-
ments* on the elastic force of aqueous vapour in air, in a state of
saturation."

The experiments referred to were made by means of an appa-
ratus similar to that described in (54). The balloon in this c

tilled with perfectly dry gas, and connected with the inanome-

The elastic force of the gas at various temperatures was deter-
mined by a series of experiments, and a quantity of water con-
tained in a glass bubble previously introduced into the balloon,
was disengaged in the usual way. The apparatus was then raised
rious temperatures, and the elastic force of the mixture of gas
and vapour observed. The elastic force of the gas being subtracted,
the remainder gave the force of the vapour, and this was uni-
formly found to be less than that derived from M. Etegnault's table?,
which, however, agreed exactlv with his experiments on vapour
•nit. The difference varied from omm.l to omn'.~, and appeared
to have no relation to the temperature. M. Reirnault Mates that

water int, into the balloon had not U-en boiled, and

was consequently 1 with air; hut it is difficult to n

the impression that the difference between the elastic force of the
mixture and the sum of the forces due1 to the Lras and vapour
parat.-ly, u;t- to the absorption of a definite p..rti..n ,.f the

gas by the water, at the co!iimen<-.-m«-Mt of the expel iment. ,
gases operated on kir and nitrogen, and the

16 Millie ill I).

R

D ours. — On comparing the

Mac's

* All!

212 EXPERIMENTAL RESEARCHES ON [BOOK I.

law of volumes, with their densities derived from direct experi-
ment, M. Dumas was led to the conclusion, that in the case of
the hydracids the volume of the vapour is always represented by
4, so that one atom of the acid furnishes four volumes of vapour.
He noticed* a striking deviation from this law, however, in the
case of acetic acid, for the density of the vapour of this body,
derived from its atomic constitution, on the preceding hypothesis,
is only 2.08, while its value, as determined by direct experiment,
at 20° or 30° above its boiling point, is 2.7 or 2.8. The diffe-
rence of these numbers being nearly equal to the density of
aqueous vapour, M. Dumas suggested as a probable explanation
of the anomaly, that the vapour obtained by the ordinary me-
thod consists of a mixture of equal volumes of pure acetic acid
vapour and aqueous vapour.

This conjecture appeared to M. Bineauf to be rendered more
probable by some investigations of his own as to the combinations
of water with the hydracids; on being submitted, however, to
the test of more direct experiments, it was not sustained by facts,
and accordingly M. Bineau subsequently^: came to the conclusion,
that acetic as well as formic and sulphuric acids do really deviate
from the preceding law, and furnish for each atom of the acid
only three instead of four volumes of vapour.

Thus the atomic constitution of acetic acid being C-iH^iOj,
we obtain

8 volumes vapour of carbon, . . . 3.368

8 volumes hydrogen, °-552

4 volumes oxygen, 4-424

Density of vapour . = — — — = 2.78

which agrees very closely with the experimental density.

So also for formic acid, whose constitution is represented by
we have

* Traite de Chimie, tome v. p. 146. f Comptes Rendus, tome xv. p. 777 (1842).
J Ibid., tome xix. p. 767 (1844).

CHAP. II.] THI-; 1H.NMTIES OF VAPOURS. 213

4 volumes vapour of carbon, . . =1.684

4 volumes hydrogen, 0.276

4 volumes oxygen, 4424

Density of vapour, ....

which, like the preceding, is in close accordance with experi-
ment; and similarly for the vapour of sulphuric acid.

Simultaneously, however, with the publication of these views,
M. Cahours* announced his discovery of the fact, that the density
of acetic acid vapour varies materially with the temperature at
which it is taken, and that the preceding anomaly disappears
completely at a temperature 100° or 1 10° above its boiling point.
Pursuing his investigations, he found that the density of this
vapour, which at 125° equals 3.20, decreases to 2.08, the theore-

••nsity, at 250°, and retains this value up to the highest tem-
perature, 338°, at which he observed it. Similarly butyric acid

•ur has a density equal to 3.68 at 177°, which becomes 3.07,
in conformity with the general law, at 261°, and remains constant
at this value up to 330°.

.M. Cahours ascertained that in the case of water, the gi
number of compound ethers, ethvlic, amylic, and mcthylic nlco-
hol, and a large proportion of the volatile oils, especially the hy-
drocarburetted oils, tin- denntv of the vapour at 30° or 40° al
the boiling point agrees V«TV well with its theoretic den>itv, de-

.ined on the supposition that its volume is represented l»v
or/'

Hut, on the oilier hand, in the ease of the following aeids

.« d from the alcohols, vi/. the acetic, butyric, and val<
and also of tin- eM6Heei of aniseed and fennel, in order to ;i
with tin- theoretic on the same supposition as to volume, the den-
sity of the vipour must be taken at tnnprraiun- al.ly
above tii«- liiiilin^ point. " It i- COliom t«« >• »•." ;i<ld> M <
hour-, "that th< , which pn-.-eiit Mich Striking aOftli
in other '-xliiliil tin- .-aiiie p« vuliai it ir> m theiT

|

mined

214

EXPERIMENTAL RESEARCHES ON

[BOOK

Bineau,* in reference to the vapours of acetic, formic, and sulphu-
ric acid. For low temperatures he employed a method analogous
to that of M. Despretz ; for those ranging from 99° to 126° he hud
recourse to the method of M. Gay-Lussac, surrounding the gra-
duated jar with saline solutions of different degrees of strength,
and consequently boiling at different temperatures, while for the
highest points he used the method of M. Dumas.

The following Table contains the results of his experiments
in the case of acetic acid.

SERIES I.

SERIES II. SERIKS III.

II

SERIES IV.

SERIES V.

t°.

/•

8.

t\

/

*• 1! e-

/•

^

5-56

5-75
6.03

3.

e.

/

S.

t\

/

*.

3-95
3-75
3-64
3.62

12.0
I9.0
22.0

2.44
2.60
2.70

3-8o
3.66
3-56

"•5

19.0

21.0

3.76

4.OO
4.06

3.88

3-75
3-72

12.0
20.0

24.0

30.0

3-92

3-77
3-7°
3.60

20.0
22.0

8-55
8.64

:::

3.88

3-85
...

20.5
28.0
35-°
36.5

10.03
10.03
11.19
11.32

The first column in each series gives the temperature of the
vapour, the second its elastic force, expressed in millimetres,
and the third its corresponding absolute density. The change
of the latter quantity with the temperature, even within the
limits of the preceding experiments, is very striking. M. Bi-
neau remarks that the results of the preceding series of experi-
ments are more deserving of confidence in proportion as the
corresponding elastic forces are greater, since any error in the
measurement of these forces by means of the kathetometer, which
might easily amount to some hundredths of a millimetre, will
have less influence on the final results according as the forces
themselves are greater.

The maximum tension of acetic acid vapour at 15° is about
7mm.7 ; at 22°, 14""". 5; and at 23°, 32min.

Where the elastic force and temperature of a vapour chanijc
together, any alteration in its absolute density may result from its
following a different law from air, either in its compression or in
its expansion by heat, or in both ; but where the pressure remains
constant, or nearly so, any considerable change in its density, as

* Annalcs <!<• Cliiiuio <•( d«' I'liysujiic (3""' Si'ric), tomexviii. p. 226.

CHAP. II.] THE DENS1TI1> t>l VAPOURS.

referred to that of air under the same circumstances of tempera-

tun- and pressure, must be referred to the difference of its dilata-

bility by heat. To understand how its expansion for a given

change of temperature may be compared with that of air in terms

of the absolute densities at the limiting temperatures, conceive

• •qual volumes, t?, of vapour and of air under the same pres-

. /, and at the same temperature, t, and let their den>

under those circumstances, referred to a fixed standard, be d and

a. Suppose now, the pressure remaining unchanged, that the

temperature of both is raised to t\ and that the volume of the

vapour in consequence becomes r', and that of the air u", their

ities now being d and d. Further, let the absolute density

of the vapour in the first instance be 8, and in the latter S'.

Then if we represent by ft the coefficient of expansion of
the vapour for the change of temperature t' - t, as referred to the
volume at the lower temperature, we have (22) v = v (i + )3), and
if ft represent the analogous coefficient for air, v" - v (i +/3').
Kuither, as the density of a body referred to a fixed standard
varies inversely as the volume occupied by a given weight, we
have

d' v v i a

a =

therefore

I Jut further,

- = 8, and — = c ;
a a

therefore

d a

7'7

and consequently

from which we obtain

to be remembered that ft nti ih< ooeffi

\pan.-i' »n .,!' mi fol (/ > \

2l6

EXPERIMENTAL RESEARCHES ON

[BOOK T.

standard. We obtain the relation between this quantity and the
coefficient for i° referred to the volume at o°, viz. 0.00366, from
the formula in page 47, by substituting j3' for »cr, t -t for r,
a = 0.00366 for k, and t for t\ which gives

g,_a(*'-Q
I + at '

Or we may obtain the value of ( i + j3') directly thus :

but

where a = 0.00366; therefore

I +at'
I +at'

and

P_«(*'-t\

I + at

Substituting this expression in the value for |3, we have

at

— I.

Applying these formulae to the results of the first and second
experiments in Series V., we find j3 = .0802, and j3' = -0255, prov-
ing that the increments of equal volumes at 20°. 5 of acetic acid
vapour and air, for a change of temperature equal to 7°. 5, are in
the ratio 3.1 : i. At low temperatures, therefore, this vapour is
very far indeed from following Gay-Lussac's law of equal ex-
pansion.

Comparing the correlative pressures and densities at the same
temperatures in the above experiments, we find :

*° =

20°.

e =

30n-

/.

S.

/•

9.

4mm.o
5 -6
8 c

3-74
3-77
3 88

6mm.o
10 .7

3-6o
3-73

•5

10 o

3.06

'y^

The density, therefore, increases much more rapidly than it

CHAP. II.]

DENSITIES OF VAPOURS.

217

should do according to Mariotte's law, and that at pressures much
inferior to those of saturation.

At temperatures superior to 250°, however, it appears that
both these laws, namely, Gay-Lussac's and Mariotte's, apply to
this vapour, since M. Cahours has shown that at those tempera-
tures the absolute density is a constant quantity.*

The results of M. Bineau's experiments on formic acid are
contained in the following Tables :

SERIES L

SERIES II.

SI:I:IKS III.

SERIES IV.

<3

f

1

f°.

f

H

|

f

fl

1

f

fi

«5°-5

20 .0

3i -5

2n"n.6l
2 .72

3 -04

2.86
2.80
2.60

II°.0

15.0

20 .O
30-5

7.26
7.60

7-99
8.83

3.02

2-93
2.85
2.69

">\5

"•5

1 6 .0
20 .0

24-5
30 .0

14.69
15.20

!5-97
16.67

17-39
18.28

3-23
3-'4
3-'3

2.94
2.86
2.76

•r.j

22 .O
29 .O

34-5

23-53
25-17
27.40
28.94

3-23
3-05
2.83

2.77

B.

e.

/

Jl

f.

/•

ft

e.

/•

. 8.

69o«nm

2.52

IOI°.0

693-

2.44

i'50-5

649™

2.20

99-5

684

2.49

IOI .O

650

2.41

"5 -5

640

2.16

99-5

676

2.46

105 .0

691

2-35

"7 -5

688

2.13

99-5

662

2-44

105 .0

650

2-33

118 .0

650

2.13

99-5

64I

2.42

105 .0

630

2.32

124-5

670

2.06

99-5

619

2.41

108 .0

687

2-31

"4 -.5

640

2.04

99-5

602

2.40

MI .<;

690

2-25

'25.5

687

2.05

99-5

a-34

I" -5

690

2.22

i»5-S

645

2.03

c.

/.

/

1.

i84°.o

75o«""

1.68

216 .0

690

* If, however, Mis probable, M. Cahours

oporatnl at thom- hi^'li tcm|M-ratiin's uii-l.-r
* pressure nearly constant, the constancy

of the absolute density only proves the ap-

: i

218

EXPERIMENTAL RESEARCHES ON

[BOOK i.

The experiments whose results are contained in Table A were
made by means of an apparatus similar to that of M. Despretz,
those in B with M. Gay-Lussac's, and those in C with the appa-
ratus of M. Dumas.

The maximum tension of formic acid vapour at 13° is about
i9mm; at 15°, 2omm.5; and at 32°, 53mm-5.

The values of )3 and |3', determined from the data in the first
line of the first column, and the mean of the last two in the second
column of Table B, are .1664 an^ -°322; proving that the di-
latation of formic acid vapour, under the circumstances referred
to, is five times greater than that of air.

Comparing the correlative pressures and densities at the same
temperatures in Table A, we find the following results :

t =

.5"-

,.

20°.

t =

«

(.

30°.

f-

I.

/

S.

/

9.

/•

9.

2""".6

7 -6
15 .8

2.87
2-93

3.OO

2mm.7

8 .0
16 .7

24. .2

2.80
2.85
2.94

8 4

'7 -5
26 .2

2.71
2.77
2.85

2.Q4

M -
J OO OOOi

booo bo '<-i

2.6l

2.70
2.76

2.8 1

'

Which prove the inapplicability of Mariotte's law to this vapour,
even at pressures amounting only to one-half of the maximum.
For sulphuric acid M. Bineau obtained the following results :

*.

/•

,

332°

690-

2.50

345

708

2.24

365

745

2.12

416
498

735
725

1.69
1.68

" Theory assigns to the vapour of hydrated sulphuric acid the
density 1.64, on the hypothesis of a combination of water and
anhydrous acid without condensation. This value agrees very

CHAP. II.] THE DENSITIES OF VAPOURS.

\\vll with the result of experiment at temperatures superior to

400°."

The great densities of all the preceding vapours at low tem-
peratures, so fur superior to those which an extensive analogy
would lead us to assign to them, and their enormous dilatubility
liv heat, joined to the fact that this disability subsequently di-
minishes, contrary to all analogy, and ultimately becomes equal
to that of air, appear to warrant the conclusion, that, even at tem-
peratures extending far beyond their boiling points, their liquids
are very incompletely vaporized. Their great dilatability would
be explained, on this supposition, by the fact, that every addition of
heat should tend to complete the imperfect vaporization, and de-
velope a fresh quantity of vapour in the apparently already vapo-
rized mass.

I Jut when the temperature is attained at which the vaporiza-
tion becomes complete, this process can no longer go on, and
the dilatability should then become equal, or nearly so, to that
of air and the other gases, as we find in fact it does.

I annot be denied that it is difficult to conceive how this
imperfect state of vaporization can coexist with the high degree

. refaction observed in some of the preceding experiments, in
which, nevertheless, the anomalies of which we have been speak-
ing, in both density and dilatation, were as striking as under
hii/her pressures. This difficulty does not, however, appear so
great as to prevent our entertaining the hypothesis in question, for
there is reason to believe that, even under the li-ehl.>t pretta
vapours undergo anomalous com lensat ions throughout their mass,
near their point of saturation.

6 li_L'ht iniidit, probably, be thrown on tin- i:
Mibjcct by an examination of the latent heat of the vapour- in
question atdiil'erent temperatu:

.M. liiin-au* appears inclined to the hypothesis, that tin
pours admit of two distinct forms of molecular ai laiu- inent.
Corresponding t«> the 5 the den-it v, the other in

which ti.- double the ma>s, and acc.TdiiiL'lv the

(3"< Seri.

220 ON THE GRAPHIC CONSTRUCTION OF EXPERIMENTS, [BOOK I.

density double the value. He further supposes that at extreme
temperatures one or other of these forms of grouping predomi-
nates, but that at all intermediate temperatures they are mixed.
These extreme densities in the case of formic acid he conceives
to be 1.59 and 3.18, and he accounts for the existence of densi-
ties superior to the latter, by referring them to the same cause
which produces those anomalous condensations which occur, as
we have mentioned, in the case of all vapours, near their point of
saturation.

SECT. VI. ON THE GRAPHIC CONSTRUCTION OF EXPERIMENTS, AND

FORMULA OF INTERPOLATION.

135. Determination of the most probable Values of observed
Quantities, from the actual Results of Experiment. — Having thus
described the principal methods which have been employed for
determining, by experiment, the elastic force and density of va-
pours at certain temperatures, it remains briefly to explain the
manner in which the most probable values of those quantities are
derived from the actual results of experiment, and also the me-
thod of calculating their values at different temperatures at which
no observations may have been made.

For, as regards the first point, experience proves that errors
are unavoidable even in the case of the simplest observations, and
where all possible care has been taken to avoid everything which
might interfere with the accuracy of the result. Thus in the
direct observation of quantities depending on a single variable, as,
for instance, of the temperature of a fluid, indicated by the point
at which the mercury stands in the stem of a thermometer im-
mersed in the liquid, or of the elastic force of a vapour, where
this is given directly by the position of the mercury in a barome-
ter tube, we find that a succession of observations of the same
quantity, under circumstances as nearly the same as possible,
always gives results differing somewhat from each other. It
is accordingly a matter of importance to ascertain how the true
value of the quantity under observation may be determined from
the actual results of experiment, or, if absolute truth is unattaina-

CHAP. II.] AND FORMULAE OF IXTEKPOLA'l 1 221

ble, to ascertain how the most probable value of this quantity,
derivable from a given scries of observations, may be deduced
from them, and also to learn the probable limits of error.

In applying the calculus of probabilities to the solution of
this question, it is assumed that all errors which result from de-
fective methods, inaccurate instruments, and peculiarities of the
observer, have either been wholly obviated, or reduced within
such limits that they will counteract one another when different
methods of observation are adopted, or when the same methods
are used by different observers. Besides these errors, however,
there exists another class, which, whether we attribute them to
imperfections of the senses, or some other causes peculiar to each
particular set of observations, unknown to us, and perhaps undis-
coverable, are found by experience to be limited in their magni-
tude, and to be such as sometimes to cause the observed quantity
to err by excess, and sometimes by defect, while the tendency of
errors of the former class, on the contrary, is always in one and
the same direction. Hence it is easy to see, in a general wav,
how a repetition of experiments, afK-eted chiefly by errors of the
latter class, enables us to obtain a more correct result. For if
there were no constant errors, and if the observations were suffi-
ciently numerous to embrace all possible combinations of the
causes produr ndar errors, as those of the second class may

Jled, and if, moreover, these causes produced in all cases equal
positive and negative errors, then the arithmetic mean of all the
observed values would obviously be the true one, or imlrrd, i
.i-ithmctic mean of the extreme observed values. 'I
supposition, i . of absolute exemption from a / i rors,

and of the existence of so numerous a series of experiment! as to
fulfil the preceding conditions with respect to ii • rrors, is

in fact never reali/'-d, and Accordingly absolute truth is unattain-
able by any single method of observation. I
fore, to multiply methods as well as observations, and to apply

< alculus of probabilities to <lc<l the most

the obser\<-<! (juun'.it v. 'I wltilfumi

the following propositions, which :', for

the int 'inuuion <•!' tho c \ .ring him for

published in

222 ON THE GRAPHIC CONSTRUCTION OF EXPERIMENTS, [BOOK I.

the second volume of Taylor's Scientific Memoirs. These propo-
sitions are applicable to the results of all those experiments in
which we observe directly a quantity depending on a single variable,
in which class are comprehended most of the experiments described
in the present treatise. The practical rules for the calculation of
the probable value of the observed quantity, so far as it can be
determined from a given series of experiments, follow directly
from the propositions themselves.

136. Rules for determining the most probable Value of a single
observed Quantity, deduced from the Method of least Squares.

PROPOSITION I. — In a series of equally good, direct observa-
tions of a quantity depending on a single variable, that hypo-
thesis with respect to the unknown quantity is most probable,
which assigns it such a value that the sum of the squares of
the remaining errors is a minimum.

Call the unknown quantity x, and suppose we have a series
of m observations assigning the values n, ri, n", &c. ; by the pre-
ceding proposition the most probable value of x is that which
renders the sum

(x - n)z +(x- nj + (x - ft")2, &c.,

a minimum. This condition, by the ordinary rules of the diffe-
rential calculus, gives

n + n + n" + &c.

x= "^ ;

and accordingly,

(a). The most probable value of the unknown quantity is the
arithmetic mean of the observed values.

Definition. — The mean error1 is that error which, if it alone
were assumed in all the observations indifferently, would give the
same sum of the squares of the errors as that which actually exists.
It is denoted by the symbol £2-

The value of the mean error is given by the equation

m - i
in which (n*) represents n2 + ri* + &c., and (n)2 = (n + n + &c.)2-

CHAP. II.] AND FORMUIJE OF INTERPOLATION. 223

Definition. — The probable error, r, of a particular class of ob-
utions, is that error below which there are as many errors less

than itself as there are larger ones above it, so that there are as

many cases in which the errors are less than ry as there are cases

in which the errors are greater.

The probable error is connected with the mean error by the

equation

r = 0.674489 to;

tliis is the most probable value of r, but it may lie between the
limits

0.476936 and 0.476936'
V 'm

orq.p.

(0.476936^ , / 0.476936^ .
! *»' ^ and r { i + — -^f-).*
Vm ) \ V("0 /

(]3). The probable error of the arithmetic mean itself is

\/ TO

If, therefore, we represent the arithmetic mean of a set of obser-
vations by a, there is an equal chance that the true value of the
unknown quantity lies between

r r

a + — — and a ; — .

V7 111 V m

PROPOSITION II. — If there be several sets of observations

Dg th«- probable values a, a, a", &c., with the probable errors
r, r', r"j &c., th«-n

* If we denote by » tin quotient ob- / 0.509 584 \

Udned by dividing the sum of all the errors, T\ ' Vm /*

without regard to their rigna, by (m- i), ^^ ^^ M appeirt ^^ ^ nM^it,,,!,,

we obtain a le« accurate value of r by of thciimit%|.l6»ftocarate than that given

ril"'''<iuat1""' inth. i.xt. I Mt, owing to the simpler nature

r = 0.845 5 of the qoan: much easier of cal-

whose limits are culatloo.

224 ON THE GRAPHIC CONSTRUCTION OF EXPERIMENTS, [BOOK I.

(a). The most probable value, A, derived from all these sets,

IS

a a a

A

(|3). And the probable error, /?, is

i

PROPOSITION III. — If X represents a known function, /, of
certain independent magnitudes, #, a?', at"9 &c., of which we know
the probable values, a, a', a", &c., and the probable errors, r, r, r",
&c., then

(a). The most probable value of JL, which we will call A, is

A =/(«, a, a", &c.)
(|3). And its probable error, jR, is

dA\* /^\2 1

isty ' +&c-j

This proposition is rigorously true for linear functions, but
only approximately so for higher ones.

PROPOSITION IV. — If X is expressed in terms of different sets
of magnitudes, a, a', a", &c., a', a', a", &c., which give, as in the
last proposition, the probable values, A, At, Aifl &c., and the pro-
bable errors, R, J?/5 Rt/, &c., then, by Prop. II.,

(a). The probable value, A, derived from all these, is

^ 4 *„

~~~

(|3). And the probable error, 1

i

CHAP. II.] AND FORMULA OF INTERPOLATION. 225

As an example of the application of the rules deduciblc from
the first two propositions, we select the following sets of experi-
ments by M Kegnault on the elastic force of aqueous vapour
ato°.

Number of Seri
iiiu-nt. / =

Series/
/=

Series h
/=

j

4-54

4.66

4-54

2 4-54 4-67

4-54

3 4-52 4-64

4-54

4 4-54 4-62

4.58

5 4.52 4.64 4.58

6 4.54 4.66 4.57

7

4.52 4.67 4.58

8

4.50 4.66

9

4.50 4.66

10

4-54

The value of a derived from Series i is a = 4.526, with the
probable error r =0.0105; from Series /, ^ = 4.653, and r-
0.0105 ; and from Series h, a" = 4.561, and r" = 0.0127. Hence
p. II.)

and

i i i

*+ ~7l

\>

4-582,

.0064 ;

accordingly the most probable value of the clastic force at o°, as

!•» drtrrimnr.l iV'im th«- pr-M-rdiii^ MT'IOS of CX|>'
ni'-nts, i- .) vS:, mid tlierc is an c«|u;il r! its posse.1-

value IM-: :S8.j and .\.^~

M.thn.l rved Values of a Scries of

QWD, '

tainrd in tin- l;i.-i , :i I'm ni-li u< \\ n li tin- ..nly kn.»\vn m<

of Co: • - of individual ol -e of

| but ifw<

2 G

226 ON THE GRAPHIC CONSTRUCTION OF EXPERIMENTS, [BOOK I.

rations of two quantities, so dependent on each other that a de-
terminate value of the one is always connected with a given value
of the other, as in the case of elastic forces and temperatures, we
possess in this case another means of correcting the results of ex-
periments with respect at least to one of the observed quantities.
This means is derived from the principle, that whenever, in the
system of physical nature, we find two quantities connected with
one another in the manner described, so that one is, in mathema-
tical language, & function of the other considered as an indepen-
dent variable, then if we vary the latter constantly in one direc-
tion, the former will vary constantly in one direction also. And
accordingly, if the different values of the quantity which is chosen
to represent the independent variable, are represented by abscissas,
and those of the other by the corresponding ordinates, the line
on which the extremities of all those ordinates will be found,
will either be a right line, or more frequently a curve of uniform
progress, free alike from sinuosities and abrupt changes of direc-
tion. The only apparent exceptions to this rule occur in cases
where, at a particular point or points, new forces are called into
play ; thus, as a general rule, we have seen that the molecules of
all bodies approximate on decrease of temperature, but in the
case of water and fusible metal, after this approximation has been
carried to a certain extent, and has reached a certain limit, the
forces which determine crystalline or polar arrangement appear
to be brought into operation, either suddenly at different points,
or gradually through the entire mass, and the decrease of tempe-
rature, if still continued, is accompanied by a remotion instead
of an approximation of the molecules ; and in a similar manner
change of state is accompanied by an abrupt change of volume.

Unless in such singular cases, however, the curve passing
througrTthe extremities of the ordinates which represent the true
values of the quantity under consideration, is a curve of uniform
progress ; and accordingly if we find that the extremities of ordi-
nates representing the corrected or mean values of observations,
lie some above and some below a curve of this description, this
law both enables us to detect the existence of errors in the quan-
tity represented by the ordinates, which might otherwise have
remained undiscovered, and also furnishes us with a means of

(HAP. II.] AND FORMULJE OF IXTKlir« 227

'•ting tin-in. For it', having marked oil' on the axis of the
abscissa' the values of the independent variable, we erect perpen-
dicular ordinaic.- representing ihe corresponding mean values of
the other observed quantities, and then describe a curve whieh
t-hall pass through one or two points determined with particular
accuracy, and among, and as near to, the rest as possible, the or-
dinates of this curve may be regarded as representing the true
values of the observed quantity, with more fidelity than the mean
values derived from experiment. And if the observations have been
uniformly distributed between the extreme limits, and have been
sufficiently numerous, and if on tracing the curve we find that it
passes between the extremities of the mean ordinates, above some
and below others, we may feel confident that it exhibits, with a
very close approximation to the truth, the relation between the
quantity under investigation and the variable on which it depends.
For an error in any mean value arises from the number of

vations from which it was derived not having been sufficiently
great to include the i'air proportion of positive and negative
errors in the obserr^l values, so that a mean will be in excess or
defect according as positive or negative errors abound in the
observations from which it was deduced; but from what has 1

as to the nature of these errors it is evidently equally pro-
bable that any mean will deviate from the true value by ex

and consequently, if the observations have been con-
ducted so as to admit only errors of the class alluded to, the curve
of the true values should pass in the manner described among the

values.
138. •• : hi/ iiriiji/iii' C<>' ( ami

•nf-r. Tli<' cum; thus described MTVCS not only t
the mean values of observation, hut :d.-<> t«» <!• tmi!
of the quantity under investigation corresponding to any a*^
value of the variable, and Ivinu between any two vahn
from OZ] we have evidently nieivlv t«»

ordii nity of a •jiven abscissa, and 1

mcnt ascertain the value .,! the quantity BOOght The

•d bv I'm

ihe .nlv with the

!rulatiiiLr the

228 ON THE GRAPHIC CONSTRUCTION OF EXPERIMENTS, [BOOK I.

required quantity. The form of this equation is in most cases
arbitrarily chosen, in some instances, however, it is determined
by theoretical considerations, and in others by some relation more
or less clearly marked between the values of the quantity sought
and the variable on which it depends. Such equations as these,
inasmuch as they cannot be regarded as representing the physical
connexion between the quantities in question, but merely as ex-
hibiting the progress of the curves which represent their relation
between the extreme limits of experiment, cannot be relied upon
much beyond those limits, and from this restriction in their use
they are frequently called formula of interpolation, as they are
also called empirical formulae, from the tentative manner in which
they are formed.

Having selected the particular form of equation which, on
trial, is found to represent with most accuracy the general results
of observation, the values of its constant coefficients may either
be obtained by assuming it to pass through the requisite number
of points on the graphic curve, or their most probable value may
be determined from the results of experiments directly by means
of the propositions in (136).

139. Methods of calculating the Constants in Formula of In-
terpolation. — For suppose the equation is of the form

bx

in which y represents the elastic force, and x the corresponding
temperature ; then if we have from the graphic curve three values,
y, y", y", corresponding to #', x", x", we obtain a, b, c from the
three equations,

bx> bx« bx">

It may be remarked that one point on the graphic curve of
elastic forces is always given by the graduation of the thermome-
ter employed in the experiments, namely, the extremity of the or-
dinatc representing the pressure corresponding to the upper fixed
point on the scale of temperatures ; thus on the centigrade scale a
force of 760™™ corresponds to 1 00°. A second point on the curve is

CHAP. II.] AND FORMULA OF INTERPOLATION.

generally obtained by the determination of the force at oc, as this
temperature is eapable of being produced with certainty and
maintained invariable for any length of time. If, therefore, we
select these two iixed points on the curve to give the values y\
.r , and y , a?'", we need ouly derive the other y", or", from the trace
of the curve itself.

Or, as we have said, we may obtain the values of the coeffi-
cients cr, 6, c directly from the experiments, by the aid of the rules
in (i 36). For, let y be the elastic force corresponding to x = o ;
then we have y = a, and therefore in the general equation,

bx

leaving only b and c to be determined. Now let y represent
the force 760""", corresponding to x" = 100°, and // the force at
any intermediate point, x", then, substituting these values in the
preceding equation, and solving for b and c, we obtain

_L__L) log!!
*; y

°y = y
'log' 'loglC

x y .1- " y

.

3 y .</

In these equations y', y" ', and x"t are suppled to K« known
with certainty : tin- only uncertain quantities ai •
then that we M-lcct ti-.-m thes.er'u-s »f «-.\ prrinn-nt - -p.-ndin^

elastic forces and temi , whose? pn>l>.il>lr raid

''«» <**', a»1(l tl.<-ir probable errors rh r\ ; n...
^m>^'w; substituting^,, "j; " . for y", .» ;.'/:n. l>y

• 11 III., in probable values for b and r, with tin
ponding pmbable errors, and from these, by IV.posir n !\

luei "1 those quaniities, as

far as they arc d.-t«-nninabl«' iV.'m tl. eted obtenrttioos,

' u. — Th-

230 ON THE GRAPHIC CONSTRUCTION OF EXPERIMENTS, [BOOK I.

pliic representation of the results of experiment is generally
effected by laying down those results on a sheet of paper, divided
by a series of engraved lines into a number of small squares.
This paper, however, as it is generally met with in commerce,
is never very accurately divided, partly owing to a want of care
in tracing the divisions on the plate from which it is printed, and
partly to the fact that, previous to taking the impressions, it is
necessary to moisten the paper, which then contracts unequally
in different directions on drying.

M. Regnault, accordingly, laid down his curves directly on a
plate of copper, divided by himself with the greatest care. This
plate was afterwards retouched by the graver, and the plates ac-
companying his memoirs were printed from it. On the copper
plate M. Regnault first traced two lines strictly at right angles,
adjacent to two edges of the plate. These lines were eight de-
cimetres in length, and were each divided by an accurate ma-
chine into 100 parts, so that the value of each division was 8nmi.
By this means the whole plate was divided into a number of
small squares, the further subdivision of which was effected by
means of a micrometric apparatus, which enabled him to appre-
ciate the one-thousandth part of each of their sides.

In the construction of the curve of elastic forces of aqueous
vapour, M. Regnault represented the temperatures by the ab-
scissa, and the forces by the vertical ordinates. " It was impos-
sible," he remarks, " to represent these forces on the same scale
through the whole range of the experiments. For at low tem-
peratures a difference of i° C. produces a variation in the elastic
force of only a few millimetres, while at higher temperatures the
same difference produces a change of many decimetres in the
force. If, therefore, we adopt for the elastic forces a unit suffi-
ciently large to render sensible the small variations exhibited by
experiments at low temperatures, these forces would be repre-
sented, at high temperatures, by lengths so considerable that
it would be impossible to introduce them into the same sheet,
and the arcs of the curve would approximate so nearly to a right
line, that their curvature would be imperceptible. If, on the
other hand, we adopt a scale sufficiently small to represent con-

CHAP. II.] AND FORMULA OF INTERPOLATION. 23 1

veniently the forces at hi«_rh temperatures, the accidental varia-
tions of experiments at low temperatures would completely
disapi

" To avoid these inconveniences I have adopted three diffe-
rent scales to represent the elastic forces of vapour within diffe-
rent ranges of temperature, but these different vertical scales all
correspond to the same horizontal scale of temperature, in which
each centigrade degree is represented by one division of the axis
of abscis-

The first scale corresponds to the range from - 33° to 5i°.6;
in this scale each millimetre of elastic force is represented on the
vertical ordinate by one division whose absolute length is 8mm.

The second scale embraces the forces corresponding to tem-
peratures from o° to 1 00°. In this each vertical division repre-
sents iomm.

The third extends from 100° to 232°; each vertical division
is equivalent to ioomm; between 100° and 197° the ordinates
I the elastic forces diminished by 760™™ ; and between
197° and 232°, the same forces diminished by io76omm.

Above 100° the mercurial thermometer does not strictly ac-
cord with the air thermometer; it was accordingly necessary to
construct two sets of curves at these temperatures; in the one the-
n-present the indications of the mercurial, in the other
air thermometer.

v point determined by direct experiment is represented
nn the plate accompanying M. Re^nanlt's memoir, by the centre
of a small cross, which is further distinguished by a letter indi-
te scries of experiments from which it was derived. \\
may remark, that the correspondence between the mean ordil

mined l>y M. Renault's expeiimrnts and the ordinates of
the mean curve corresponding to the same abscissae, is as close as
>een expected from the accuracy of his methods and
his skill as an observer.

i .} i . Classification of for t/ie <

Force of aqueous 1 I .eater number of the formula-

which have b.-rn proposed to i ' the relation , the

clastic force of aqueous vapour and its temperature. ha\ e l>een 1
on Dah»n's ! ted to ( ' -uelv. that within

232 ON THE GRAPHIC CONSTRUCTION OF EXPERIMENTS, [BOOK I.

the limits of experiment the elastic forces of aqueous vapour are
represented by the terms of a geometric series with constantly de-
creasing ratio, when the corresponding temperatures form an
arithmetic series with equal differences.

For convenience of enumeration we may divide these for-
mulae into the following classes :

In the first the force is represented by the general term of a
series, in which each successive term is formed by the multipli-
cation of the preceding by the ratio diminished by a quantity
depending on the number of the term. This form is a direct
and simple algebraic statement of Dalton's law. The general
expression is

y = yoa(a-b)(a-2b) (a - (x - 2) I),

in which y is the general term of the series of forces correspond-
ing to the oc*h term of the series of temperatures, ?/o the first term
of the forces, a the first ratio, b the quantity by which each pre-
ceding ratio is constantly diminished.

In the second class the force is represented by the general
term of a geometric series with constant ratio, modified by the
addition of certain terms to the exponent of the ratio, so as to
produce the retardation in the progress of the series required by
Dalton's law. The general term of a geometric series with con-
stant ratio being y = z/o^> in which ?/, yo have the same significa-
tion as before, r is the constant ratio, and x the number of the
term diminished by 2, the general expression of formulae of the
second class is

mi — y ^a + 6* + CX2 + rf*S+&C.

In the third class the force is represented by the sum of the
general terms of different geometric series ; the expression is of
the form

y = a" + x* + or-'*** + a»"^"* + &c.

In the fourth class the retardation of the geometric series is
effected by dividing the exponent of the ratio by a linear function
of the same exponent; the general term has the form

''

CHAP. II.] AND FORMULJE OF INTERPOLATION. 233

In tl\Q fifth the forces are supposed to form the terms of an
ordinary geometric scries, when the temperatures constitute a
similar series, but with a different ratio. The general expression
in this case would be y = Axm, which, further generalized, be-
comes

In the sixth the general term is formed by a combination of
the forms in the second and third class ; its general expression
is

., _ gfl «• Aaf + B$t • C-)t &c.

142. I. Formutit: whose general Expression is y = i/oa(a-b)
(a-2b) ..... {a-(x-2)b}.

(i.) Mr. Dalton* employed a formula of this class, in which
the temperature was not counted by degrees on any of the scales
usually adopted, but by intervals of 5° Reaumur, or 1 1°.25 Fahr.,
counted from 32° F. Let /^represent the elastic force in Eng-
lish inches of mercury, corresponding to any temperature ex-
pressed by T of these intervals ; f the force at 3 2° F. ; then for
temperatures above 32°,

and below 31°,

a (a + b) (a + 2/>) ...:•' (T \
in these expressions / = 0.2 inch.

0=1.4872, £ = 0.01567, a' = a + b= 1.5029.

M r. Uref adopted a -iinilar formula, differing from Mi

Dah • ly in tin- vain-' of the arbitrary decrees by which lie

«\ pressed the temperature, and in the jh/mt from whieh hr

i istcd of intervals of 10° F., an<l

:ic', tli- io, a= 1.23, and the con

.01.

'

1818, Part ii., p. 350.

234 ON THE GRAPHIC CONSTRUCTION OF EXPERIMENTS, [BOOK L

Above 210° F. the expression, therefore, is,

F=fa(a-b) (a-2b).... {a- (T- i) />\ ;
and below 210°,

*%(« + *) (a*,*/ <a+(T ,)*}'

in which/, the force at 210°, = 28in.9, a = 1.23, b = o.oi.

To preserve the law of continuity in this formula, as was re-
marked before, the first divisor giving the force at 209° should be
1.24 instead of 1.23, and accordingly the values of a and b should
be modified so as to exhibit this continuity in the formula.

Formula? of this class are very badly adapted for the purposes
of interpolation. To obtain any term it is necessary to calculate
all those preceding it; moreover, they cannot be immediately ap-
plied to fractional parts of the arbitrary units of temperature, for
which they are constructed, and consequently will not give the
forces corresponding to assigned degrees on any of the ordinary
scales.

1 43 . II. Formula ivhose general Expression is y = ytf* +bx* cx* lSrc-

(i.) M. Laplace* first proposed a formula of this class, in which
the exponent consisted of two terms. His formula is

in which t, the temperature, is expressed in centigrade degrees
counted from 1 00°, the boiling point of water under the pressure
/= ora.76. These degrees are positive above 100°, negative below.
Fis expressed in metres of mercury. M. Laplace calculated the
values of p and q from Mr. Dalton's experiments, and found
p = 0.015457, q = o.ooo 062 582 6. Reduced to logarithms this
expression becomes

Log F= log om.76 + 0.015 457 t - o.ooo 062 582 6 t2.

If we express the temperature by centigrade degrees counted
from o°, this formula becomes

Log F= log 0^.005 123 -f 0.027971 2 t- 0.000062 585 26 £-,

* Mccanique Celeste, tome iv. p. 273 (1805).

CHAP. II.] AND FORMULAE OF INTERPOLATION.

in which om.oo5 123 represents the force of aqueous vapour at
o°C.

(ii.) M. Biot* proposed a formula ol' this class, with three
terms in the exponent. He ealeuhited the values of the constants
from Mr. Daltun's experiments. Expre.-sing the force in Eng-
lish inches, and the temperature in Fahrenheit decrees, counted
from 212°, positive descending, and negative ascending, his for-
mula is

Log F= Iog3oin -0.008541 21972^-0.00002081091 t-
+ o.ooo ooo 005 80 £*.

Interred to French measures this formula becomes

Log F= logom.76- 0.015 372 787 57 t - 0.000067 3!995 *'~
+ o.ooo ooo 033 74 <3,

where F is expressed in metres, and t in centigrade de;_ •:•
counted from 100° C., positive below this point, and negative
abo\

On calculating the values of the constant cocllicients in M.
s formula, from Mr. Ore's observations, Mr. Ivoryf obtained
the following expression,

Log F = log 30'" + 0.008 746 6 t - o.ooo 015 178 I-
•f o.ooo ooo 024 825 £3,

in \\hirh /•' is Wf] M Knglisli inches, and / in Pahienheit

;ees, counted from 21 2°, positively ascending, m-i-at i \el\-

If we di-.-iiv I-. mak<- tlie degrees positive d«>crnd-

as in M. Ui-it'.- I'Tinuhe, it is «»nl\ iir<v — .uv t" elian-j"' th|%

- of I and

This cxpiv.Vi.iii may l>e put under the f,,iiu

1,1,1 i,,.

< ..|,.n,ii;,,il,-.ui, Su| 'i 17060, h =-. -

i ! 000020812 37, cr- f. ooo ooo 005 805.
i. ban rcmark> -i. tl...t in con- t riiil<>*>|>lmnl M.I;;..

' : . , .

236 OX THE GRAPHIC CONSTRUCTION OF EXPERIMENTS, [BOOK I.
p

- represents the force expressed in atmospheres of thirty inches,

and the first member of the equation is the ratio of the logarithm
of this force to the temperature. If this ratio were constant the
elastic force would increase in geometric progression when the
temperature increased in arithmetic ; the terms affected by t and
t2 represent the deviation from this law.

144. III. Formula: ichose general Expression is y = a^iXx +

a/i'-\'x + aM" + X"* + SfC.

M. Prony* applied formulae of this kind, with two, three, and
four terms, to represent the experiments of M. Betancourt. As
the results of these experiments, however, were not very accurate,
we do not consider it necessary to give the numerical values of
the constants as determined by M. Prony.

1 45 . IV. Formula; whose general Expression is

(i.) Professor August,f of Berlin, proposed a formula of this
class, with two terms in the denominator of the exponent. It
was, accordingly, of the form

In this formula there are three constants to be determined,
/, a, and /3 ; / is evidently the elastic force corresponding to a
temperature = o° ; this being known, we only require two addi-
tional data to determine a and )3 ; one of these is given by the
construction of the thermometric scale which we adopt, on which
a certain arbitrary temperature is assigned to the vapour of water,
when it has a certain pressure ; the other may be derived from
experiment. M. August, however, determined it from the suppo-
sition that vapour loses its elastic force at the absolute zero, which,

as we have soen (62), has been fixed at - 266°-. On this sup-
position we have F= o, when t-- 266°-, which gives 1-266 ft

* Nouvcllc Architecture Ilydrnulique, § 1522.
| FoggeudoriTs Annalcn, vol. xiii. p. 122 (1828).

CHAP. II.] AND FORMULA OF INTERPOLATION. 237

= o, and /3 - i -f- 2662 = 3 -^ 800. Adopting the centigrade

, we have F= ora.76, when t = 100°. Substituting these va-
lues t'..r /' and t, and lory' the value om.oo5 057 8, determined

ly M. (iay-Lussac, and for/3 the number - bovc, we have,

ooo

to determine a, the equation

om.76 = ora.oo5 057 6 a ll ,
whence

/ 076 V1 —

a = ( - ~~T/800 = ( 1 50.26o)«oo ;

substituting this in the general equation, we have

nt
F= om.cx>5 057 6 (150.263)^^.

Reduced to the logarithmic form, this expression becomes
LogF= log (0.005 °576) + 5~~ ~~y l°g(1 50-263),

OOO *r *<'

or

800 -t- 3^
and solving for £,

800 2.296 055 5 + log /•'

* xV\ 1 ' *

This {'unnula represents the force of aqueous vapour with
considerable acmracv, llihoogb we have reason to believe tli.it
tin- jniiiriplr In-iii which tin- value of /3 was drrixvd is rrr..-
ncous. This is owing t«> th.- t-in-umstancc, that the j...int at
acjueous vapour loses its clastic force, although n.-t that
prul)al,ly very l..\v, and that lh«- fnellii-i«-nt p i> u-.r
very inlhirntial in the li.nnula.

proposed a similar lonnula, \vh.«se OOn-
i-, with tli- -ii of one, he deteHDJ nain

S3°)«

238 ON THE GRAPHIC CONSTRUCTION OF EXPERIMENTS, [BOOK I.

theoretic considerations, which arc neither very precise nor ac-
curate. The remaining constant he obtained by comparing his
formula with the provisional table compiled by the Academy of
Paris in 1823, prior to their experiments in 1829.
M. Roche's formula is

lint

in which F is expressed in atmospheres, and t in centigrade de-
grees, counted from 100°. To n he assigned the value 0.0155 ;
the Commissioners subsequently found that the value 0.0149
agreed better with their experiments, and M. Roche finally adopted
0.0152, which gives

0-167*

The accordance of this formula with the results of experi-
ment can only be explained, as in the preceding case, by the
fact that the more important coefficients are determined, directly
or indirectly, from experiment, while those derived from theore-
tical considerations are less influential.

(iii.) Professor Magnus* has also adopted a formula of this
class, all the constants in which he has determined from his own
experiments, applying, as in (139), the method of least squares.
His formula is

7-4475 f

F« 4.525 (io)8M-wtS

where F is expressed in millimetres and t in centigrade degrees,
counted from o°.

146. V. Formulae whose general Expression is y = 1/0(1 f />,/•)'".

If, instead of supposing the elastic forces of vapour to consti-
tute a, geometric scries with a decreasing ratio, when the tempe-
ratures form an arithmetic scries, we assume the forces and
temperatures to form the corresponding terms of two ordinary
geometric scries, witli different constant ratios, we obtain for the
force an expression of the form F = At1" : for the general term

* Taylor's Scientific Memoirs, vol. iv. p. 234.

CHAP. II.] AND FORMULAE OF INTKHPol.A I : 2 }»;

in tlic scries offerees is F= ar", and the corresponding term in
•A' temperatures is t = aV". Eliminating n we have

where

m = log - and ^ = - — .

0 '"

(\.) Mr. Tregaskis* proposed a formula of this kind. II.
supposed r - 2 and / = 1.2; hence in = 3.8, and counting the
temperature on the centigrade scale, starting from o°, and taking
the force corresponding to 100° as unity, we have

F= too-3-8*3-8.

This formula is not found to accord well with experiment,
\\V have referred to it for the purpose of connecting the preccd-
ing formulae with those which follow, and which may, in fact,
be considered generalizations of it.

(ii.) Dr. Youngf appears to have been the first to propose a

formula of this latter class, whose general expression, as we have

iked, is F=f(i + bt)m. In this formula, as in all of the

-, /represents the force at the point from which the tempera-
ture is reckoned. Counting from 32° F., and using KiiLrli>h me*
. I )r. Young's formula^ was

^=0.1781 (i + 0.006. *)7.
(iii.) Tredgold§ adopted the following formula of this cl

F-

'77

in KnL/lish measures, which, being reduced to the , i,-m,

and ! /rude scale, becomes

F= .18 + .007 t f .000 it,

.Mir.il Phil-. 400. / l'i-iii;; i-Miiiili-l :i, II|H.V('.

§ Treatise on the Stc.r 1 838),

240 os THE cnArnic CONSTRUCTION OF EXPERIMENTS, [BOOK i.

in this F is expressed in centimetres of mercury, and t is counted
from o°.

All formulae of this class admit of being simplified by taking
as the unit the force at the assumed o°, since /in that case be-
comes = i , and the general form is F = ( i + bi)m.

Thus in the preceding formula of Tredgold's, if we count the
temperature from 100°, in units of 100° Cent., and take as the
unit of force an atmosphere of seventy-six centimetres, the ex-
pression becomes

F =(1+0.57 14 O6-
(iv.) M. Coriolis* proposed the formula

fi +0.1878 A5-355
F= \ 2.878 ~J '

in which the force is expressed in atmospheres, and the tempera-
ture in centigrade degrees, counted from o°. If t be counted
from 1 00°, this formula becomes

F= (i + 0.006525 O5'355*
and if t is counted in units of 100°,

JP=(i + 0.6525 O5'355.

(v.) Mr. Southern! adopted a formula of this kind under the
logarithmic form,

Log F= S-T3 loS (« + 5 i-3) - I0-94i 23

where t is expressed in Fahrenheit degrees, and F in English
inches.

This formula is equivalent to

+0-019 49 -*\5'13
2^ ) '

which is of the same form as that proposed by M. Coriolis.

* Mecfttriquc dcs Corps solidcs (1844), f Robison's Mechanical Philosophy,

p. 190. vol. ii. p. 172.

CHAP. II.] AND FORMULAE OF INTERPOLATION. 24 [

(vi.) The French Commissioners* also adopted a formula of
this class,

*- (I + 0.7153.*)*

in which the force is expressed in atmospheres of ora.76, and t is
counted from 100° in units of 100 degrees.

They have remarked, however, that for the lower part of the
scale- Mr. Tredgold's formula agrees better with the results of ex-
periments, and accordingly they have employed the two formulas
in the calculation of their tables, — Mr. Tredgold's, as far as four
atmospheres, and their own beyond that pressure.

If, instead of assuming arbitrarily the exponent in the preced-
ing formula^ as has generally been done, we determine both it
and the coefficient of the temperature from two extreme observa-
tions, as, for instance, from the forces at o° and 224°, we obtain,
as Sr. Avogadrof has shown, the expression

F=(i + 0.5 706. O5'94,

which may be expected to accord better with the whole range of
observations than either the Commissioners' or Mr. Tredgold's.
All formulae of the class F= (i + bt)m represent the force as be-

coming equal to cypher when t = - ^; if we count the temj

turcs from this point we have

F = ctm,
where c = bm.

Applying this modification to the last formula, we obtain

.F=o.c

where t is counted from - 75°-25 C. in units of 100 degrees.

American Commissioners^ found the results of

their experiment! ivpivsmtrd l.y the formula

F=(i +. 00333 08»

in which /•' is ezp :'i atmospheres and t in Fahrenheit de-

grees, counted from 2i2°.§

' A final™ ^que, . \.-l.

tome xliii. p. 107 (1830).

- IIMIlriT-.... 1 ;il

p. 325. In.). (•> a f,,im '!•«•, propose* 1

242 ON THE GRAPHIC CONSTRUCTION OF EXPERIMENTS, [BOOK I.

147. VI. Formula whose general Expression isy=en+ AaX+ BPX* &c-
— M. Biot has given in the Connaissance des Temps for 1844
a table of the elastic force of aqueous vapour, calculated by
means of a formula of this class. His formula is

Log F = a - ba< - c/3'.

He has based the determination of the five constants on ex-
periments of M. Gay-Lussac's between - 20° and 100°, and on
those of MM. Dulong and Arago between 100° and 220°. Their
values are

a= 5-9<5l3I3302559

Log b = 7.823 4°6 88 1 930

a =-0.013 097 342951

Log c = 0.741109518370

|3 = - 0.002 125 105 843

In this formula t is supposed to be counted from - 20° on
an ideal air thermometer, whose indications are derived from
those of the mercurial thermometer by the relations assigned by
MM. Dulong and Petit.j This thermometer is supposed to mark
100° at a temperature corresponding to that of aqueous vapour,
whose elastic force equilibrates the weight of a column of mer-
cury equal to 76omm at o°, under the influence of gravity at
Paris.

148. M. RegnauWs Formula of Interpolation. — M. Regnault
has employed three formulas of interpolation adapted to different
parts of the thermometric scale.

(i.) Between - 32 and o° he has employed the formula

F=a + bdr, (E)

in which T is reckoned from - 32, so that T = t + 32°. The con-
Mr. Alexander in the Philosophical Maga- f Additions a la Connaissance des Temps,
zine for January and February, 1 849. The p. 8 (1844). In reducing the indications
reasoning by which the author attempts of the mercurial thermometer to those of
to deduce the constants from theoretical the ideal air thermometer, M. Biot has as-
considerations is a mass of mathematical sumed that the indications of different mer-
and physical blunders, and the formula it- curial thermometers are always strictly
self fails to exhibit with accuracy the re- comparable, which, however, M. Reguault
suits of the most trustworthy experiments has shown not to be the case,
at high temperatures.

CHAP. II.] AND FORMULA OF INTERPOLATION. 243

^unts were determined from the three following data given by
the graphic curve,

£ = -32 T= o F=omm.^2
t = - 16 T= 16 F= i .29
t= o r = 32 F=4 .60
lie nee

Log b= 1.602472 4 Log a = 003 3980
a = 0.080 38

(ii.) From o° to 100° he adopted the formula

LogF = a+£a'-c/3', (D)

similar to M. Biot's in (147). In this t is counted from o°, and
the constants were determined from the following data of the gra-
phic curve:

t = o

F = 4mm.6o

*= 25

F= 23 .55

;= 50

F= 91 .98

t= 75

/"= 288 .50

* = 100

F= 760 .00

II« no-

Log a = 0.006 865 036
Log/3= 1^9967249
Log b = 2.1340339
Log c «= 0.6 1 1 648 5
a = + 4.7384380

(iii.) I4'n>m 1 00° to 230°, the formula which he u^ed was

Log F=a- be? - c|3T, (II)

in which T = t + 20, t l»ein«_r the crnti%Lrrade trinpt-ratuiv eounte«l
from 0°. This lormula miuht al.-«» have IMMMI employed to cal-
culate the forces thn.u-h the wh«,l,- range Ir^in |o° t.» 230°,

as it rep i fchem with considerable lid that be-

tween - 20° and 40° it gives values a littlr 1. <> than the true

Th. -illation of the constants were,

t = - 20 F» O"

t= 40 /•' 91

t e 10O A' - 760 .OO

244 ON THE GRAPHIC CONSTRUCTION OF EXPERIMENTS, [BOOK I.

t = -i6o F=> 465imm.6o

t = 220 F =• 17390 .0

and hence

Log a = 1.994049292
Log )3 = 1.998 343 862
Log 6 =0.1397743
Log c = 0.692435 i
a = 6.2640348

In these three formulae the temperatures are supposed to be
counted on the air thermometer, which for the first two (E), (D),
may be supposed to coincide with the mercurial.

149. Formula? for the elastic Force of the Vapours of various
Liquids. — Sr. Avogadro* has found that the elastic force of the
vapour of mercury is represented with considerable accuracy, be-
tween the limits of his experiments, by the formula

Loge = - 0.64637 t + 0.075 956 & ~ 0.18452^,

in which e represents the elastic force expressed in atmospheres
of 76omm, and t the temperature as given by his mercurial ther-
mometer, in units of 100° C., counted from 360°, the boiling
point of mercury, positively towards o°.

The same author has calculated the following formulae for the
elastic forces of the vapours of alcohol, spirits of turpentine, and
ether, from the experiments of M. Despretz :f

For alcohol,

Log F '= log om-76 + 0.018023 t - o.ooo 14634^;

For spirits of turpentine,

Log F = log om-76 -f o.o 1 1 608 t - o.ooo 09 1 083 t2 ;

For ether,
Log F- log om.76 + 0.014848 3 t - o 000014 595 t2.

In these formulae F is the elastic force in metres, t the tem-
perature in centigrade degrees, counted from the respective boil-
ing points of the liquids, positively, ascending.

Comparing this latter formula with that for the elastic force of
aqueous vapour similarly expressed, namely (p. 235),

* Avogadro, Fisica, tomo iv. p. 420. f Ibid., p. 416.

CHAP. II.] AND FORMUUE OF INTERPOLATION. 245

Log F= log om.'j6 + 0.015 372 8 i - 0-000067 32 f~,

we see the approximation towards Dalton's law of equal"pressures
at temperatures equidistant from the boiling point, exhibited in
the case of water and ether, as the coefficients of 'the first power
of the temperature are nearly equal in those two formulae.

As we have mentioned (138) that formulae of interpolation
can only be regarded as exhibiting the curve of values of the un-
known quantity icilltin the limits of experiment, we have not
thought it necessary to discuss the form of the curves represented
by the various formulae in the preceding pages, beyond those li-
mits, or to notice the singular points which they present. Any
person desirous of pursuing this subject will find it fully dis-
cussed by Signer Avogadro in his valuable work on the physics
of ponderable bodies.*

150. Explanation of Tables 7., //., ///. (i.) Method of ex-
presfdn-/ (/»' /' //<y n/////v in tiiese Tables. — We now proceed to ex-
plain the construction and arrangement of the following tables.

The first three tables give the elastic force of aqueous vapour
within diHcrem limits of temperature, calculated from M. I;
nault's experiments.

In these tables the temperature is supposed to be determined

by means of a standard air thermometer, corrected for the expan-

uf its envelope, and graduated according to Fahrenheit's

scale, the point marked 212° on which corresponds to the tem-

:ture of the vapour of water boiling under a pressure equal
to that which a column of mercury thirty inches high at 32° F.
would pioduee under tli-- equator and at the level of the

Material of standard Thermometer. — We have selee:
the standard an »///• thermometer^ because, as has bccMi previously
remarked, it is the only one whose indications can be relied upon
at hiLfh temperature.-. Thi> in.Mi um.-iit may be constructed either
on the principle of the expansion of air \>\ heat under a con
. or on that of the increase of its elastic force o\\
.-amc cause, »tant volume. Of these \\\^

principles, M. Ive^nault recommends i the latter.

An air them ;cc<.idiiiLr to this method, will

''r'-355i 4°^

246 EXPLANATION OF FOLLOWING TABLES. [BOOK I.

resemble in its arrangement the form of apparatus represented in
Figs. 36, 37, and described in page 84. Where the thermometer
is designed to measure very high temperatures, M. Regnault re-
commends that it be rilled, in the first instance, with highly rare-
lied air, so that, when heated, its elastic force shall not much
exceed that of the surrounding medium. In this way we obviate
all danger of alteration in the form and volume of the reservoir,
arising from excess of internal pressure at high temperatures,
when the material of the envelope might be partially softened by
heat.

The value of the coefficient of dilatation of air for i° of our
standard thermometer is 0.002 036. This is the quantity which
should be employed in calculating the temperature from the data
of the instrument. If we adopt in its construction the principle
of the expansion of air under a constant pressure, the value of the
coefficient would be a little greater, namely, 0.002 038 7.*

Where extreme accuracy is required, the amount of the cor-
rection to be applied for the expansion of the envelope should be
determined by previous experiments in each particular case. In
most cases, however, it will be sufficient to derive this correction
from Table VI. , which gives its amount for flint glass, and for
such specimens of ordinary or crown glass as do not contain a
sensible quantity of lead.

Although the best adapted for a standard, however, the air
thermometer is not at all fit for general use. Every observation
made with this instrument is in fact an experiment. For general
use, accordingly, we must have recourse to the mercurial ther-
mometer, graduated, however, not independently, but by compa-
rison with a standard instrument. Between 32° and 212°, indeed,
the indications of a mercurial thermometer, graduated indepen-
dently, may be considered as identical with those of one filled with
air ; but beyond 2 1 2°, as M. Regnault has shown, the peculiar na-
ture of the glass forming the envelope of the mercurial thermo-
meter aifects its indications in such a manner as to render a

* These values are obtained from the tor 0.555 497, which, as we shall see in

coefficients corresponding to i° of M. Reg- p. 250, expresses the ratio of a degree on our

nault's thermometers, scil. 0.003 665 and thermometer to one on his.
0.003 6?> by multiplying them by the fac-

HAP. II.] EXPLANATION OF FOLLOWING TABLES. 247

particular correction necessary for each instrument. Accord-
ingly, the indications of a mercurial thermometer should be cor-
rected by direct comparison with an air thermometer in all cases
in which extreme accuracy is sought to be obtained ; in others
it may be sufficient to apply a correction depending on the general
nature of the glass of which the envelope is formed, the amount
of which is given for four different kinds of glass in the seventh
of the following tables.

(b.) Method of Graduation. — It is with considerable reluc-
tance that we have employed in these tables Fahrenheit's scale,
the only advantage possessed by which, namely, the convenient
magnitude of its unit, is far more than counterbalanced by the
inconvenient position of its zero, and the arbitrary number of
divisions introduced between the fixed points. British men of
science, however, appear so unwilling to adopt, even in scientific
treatises, a system different from that universally prevalent among
practical men, that we have felt we should only diminish the
utility of the following tables by deviating from established usage
in this respect.

(c.) Method of determining upper fixed Point. — As the tempe-
rature of the vapour of boiling water varies with the pressure to
which it is submitted, and as the weight of a mercurial column of
a given height, by which this pressure is usually measured, v
with the force of gravity, at different latitudes, and di Hi-rent
heights above the mean level, it follows that in order to render
the upper fixed point in the graduation of the thermometer ab-
solutely determined, we should specify the latitude and elevation
at which a mercurial column of given height is supposed to re-
normal pressure. \V. h;lve selected for this pur-
pose the latitude ofo°, and the level of the sea, and accordinidv
the normal pressure adopted f<>r the graduation of our standard
thermometer is that which a column of mercury of thirty in.
}iiLrh, at the temperature of melting 106, would have at the le\.-l
of the sea, under the equator.

To find t it of the Corresponding column at any latitude

and at the -am-' level, it is only necessary to multiplv } >' l>v the
ratio ofthc force of gravity at thce.juator to its force at the Lriven
latitude. In tin- way we can n-adily find the baroinetrie juv

248 EXPLANATION OF FOLLOWING TABLES. [BOOK I.

£t which a thermometer should be graduated at any latitude, so
as to agree with our standard. As it is impossible, however,
without the help of apparatus similar to that represented in Fig.
60, to command the requisite pressure, the following method of
determining the point on a given mercurial thermometer, corres-
ponding to 212° of the standard, will be found at once most accu-
rate and most convenient.

(d.) Method of finding the Point on a given mercurial Thermo-*
meter corresponding to 212° of the Standard. — The stem of the
thermometer being divided into portions of equal length, marked
on the tube itself, and the point corresponding to 32° carefully
determined, the instrument is plunged in the vapour of boiling
water, in a vessel similar to that represented in Fig. 34, so that
the whole of the mercurial column is brought to the temperature
of the vapour. The division on the tube at which the mercury
stands is then noted. The height of the barometric column and
its temperature are next observed, and this height is reduced to
the equivalent at 32° by means of the fifth table.

If the place of observation is at any considerable height above
the level of the sea, the length of the barometric column at 32°
must be reduced to its equivalent at that level, by multiplying
it by the ratio of the forces of gravity at those two positions.
This ratio is given by the expression*

in which g is the force of gravity at the sea-level, g the force at
the height h, and r the mean radius of the earth. Accordingly
it' I represents the length of the barometric column at the height
h above the mean radius, the length of the column of equal
weight at the sea-level will be

1 i ( $h\

7- , or g. p. = I { i - — 1.

\

4?'>

This length is next to be reduced to the length of a column
of equal pressure at the equator, by multiplying it by the ratio

* Poisson, Mecanique, tome i. p. 459.

CHAP. II.] EXPLANATION OF FOLLOWING TABLES. 249

of the force of gravity at the place of observation to its force at
the equator. This ratio is given by the formula

G'=G(i +71 sin2 A),

in which G' represents the force at the latitude X, G the force at
the equator, and

n = 0.005 3 13 2; log n= 3.725 3561640.*

So that if I be the length of the barometric column, reduced to
32°, at the place of observation, and L the length of the column
of equal pressure at the sea-level at the equator, we have

-i +tiBin»A).
4*7

Having thus found the pressure, in inches of mercury at
the equator, under which steam is formed at the time of observa-
tion, a reference to Table III. gives the corresponding tempera-
ture as marked by our standard thermometer. This temperature,
therefore, is that corresponding to the point noted on the thermo-
meter under comparison, and hence the value of each division on
its stem, and the point on it corresponding to 212° on the stan-
dard, are readily round.

ii. Method of expressing elastic Forces. — The elastic forces of
aqueous vapour are represented in the following tables by the

•hs of mercurial columns of equal pressure, both at the equa-
tor and also at the latitude of Dublin (53° 21' N.) From the
mer, namely, the lengths of mercurial columns which wt-ultl
equilibrate the clastic force of the vapour at the equator, the
corresponding lengths at any latitude may readily be obtain- «1
by dividing the values given in the tables by the quantity
1 ' ^-005 3132 sin- A). For Great Britain the. values c«.»nta'

.iluc ofaisilrt.Tmin.--l, l>yHMUU <#fc Memoir*. v..l ii. |>. }S;.

of Clairaut's theorem, from th •• », deduced from Bowditch's f«rm

earth'* cllij l-xiuced the length of the pendulum vibrating se-

l»y Il«'.ss«'l from a roiii|.ari-on <-f th«- ni"St on, hat various latitudes, el.*'* not dill, r

recent arc-measurements. The value of much from the preceding ; it is a =

tli" mean radius, according to the same 0.0053329 — Botcditch'$ Laj>

authority, i.s 20888012.077 English feet, p. 284.
or 6y>' trcs — Tayl

* 2 K

250 EXPLANATION OF FOLLOWING TABLES. [BOOK I,

in the column for Dublin will be found sufficiently accurate, as
its latitude is not far from the mean latitude of these islands.

With respect to the degree of accuracy with which the pres-
sures are sought to be expressed, it is obvious that it is unneces-
sary to affect a greater accuracy than our means of measuring
temperatures will enable us to realize. Thus if the smallest change
of temperature which a thermometer can estimate is the one-tenth
of a degree Fahr., and if the change of pressure corresponding to
this change of temperature at any part of the scale is cAooi, it is
clearly useless to carry the values of the pressures beyond three
decimal places at that part of the scale ; and as the change of
pressure for i°, under those circumstances, willbeo'.oi, it follows
that we may omit the fourth decimal as soon as the difference of
the pressures expressed with four decimals equals i oo ; and simi-
larly, if the smallest appreciable change of temperature is one-
twentieth of a degree, we may drop the last decimal where the
difference for i° equals 200; in general, if i -r-nth of a degree is
the smallest quantity capable of being estimated by the thermo-
meter, we may omit the last decimal as soon as the difference for
i° equals 10 n of the units expressed by figures in that place.
We have supposed one-fiftieth of a degree Fahr. to be the
smallest change of temperature capable of being determined
with certainty,* and have, accordingly, in the following tables
retained the last decimal figure until the change for i° exceeded
500.

(iii.) Method of Calculation. — It now remains to explain how
M. Regnault's formulae were adapted to the calculation of the
following tables. In the first place it was necessary to determine
the point on his thermometers corresponding to 212° of our stan-
dard, that is, the temperature as marked by them, corresponding
to a pressure equal to that of thirty inches at the equator. Now
thirty inches equal 76imni.9862, and a column of this length at
the equator is equivalent to one of 7$9mm.6()82'j at the level of
the sea at Paris, and to one of 7 $9™™. 7 07 2, at the observatory,
which is about sixty metres above that level. On reference to

* It may be remarked that M. Rcgnault of i -f- 20oth of a degree Cent., or about
states that one of his thermometers was i -H looth of a degree Fahr.
capable of indicating with accuracy a change

(HAP. II.] I'LANATION OF FOLLOWING TABL1

M. Kegnault's table.-. \vo iind that a pressure of 759'nln.7O7 cor-
responds to a temperature of 99°.9895» which is, accordingly, the
point corresponding to 212° of our standard, and hence i° of
the latter equals o°.555 497 Cent., and t° C. = .555 497 T° Fahr.
In Regnault'fl formulae the elastic forces are expressed by the
length in millimetres (F) of the equilibrating column of mercury,
at the latitude of Paris (48°5o'i4") and at the height of sixty me-
tres above the level of the sea. The equivalent length in English
inches (/) at the level of the sea, and under the equator, is given
by the expression

i +n sin2 48° 50' 14"
i = JF (0.039 370 79) - — £-

i + —
4'1
since ilnm = o'.o39 370 79.

Substituting the values for w, /*, and r, we get

i = ^(0.039488 9),

and log i = log F + 2.596 474 838 2.
Hence formula (D), namely,

Log F = a + ba* - f/3/,
becoi;

Log i = 2.596 474 838 2 + a + /
or

Log i = ait -f t>ar - /•/j//,

aH = a + 2.596474838 2

L°ga,, = -555497 1"
Log

and '/'d«'Mot<^ tin- iiuinl). :

and ci.unt.'d I'DMI the ^-aine zero.

KieH th-1 I'-'ivr in iiu-hi\< / at Dul)lin \ve 1

i -»- n sin* 53°. 2 1 1.003420003'
I .og it = log t - o.oo i 482 75 1

M. Kr-llail!'

him

252 EXPLANATION OF FOLLOWING TABLES. [BOOK I.

calculated by means of logarithmic tables extending only to
seven places of decimals, are not as accurate as if they had been
computed by the help of more extended tables. Previously,
therefore, to adapting those formulae to English measures, we
calculated the values of their constants from Vlacq's tables, in
which the logarithms are given to ten places of decimals. The
following are the resulting values of the constants:*

In Formula (D). In Formula (H).

a = 4-739 389 852 7 a = ^2<53 5°9 686 5

Log at = 0.006 864921 i Log a, = 1.998 343 377 8

Log j3,= 1^.996 725 549 5 Log f3, = 1.994 048 173 7

Log b =2.1319476110 Log b =0.6924504192

Log c =0.6117426630 Log c =0.1395539584

In Formula (E).

a = - 0.082 094

Log b = 1.604 327 6 b = 0.402 094

Log at = 0.033 316014 a, = 3.412 371 i

These values reproduce the data from which the constants are
derived, with a much nearer appproach to accuracy than those
given by M. Regnault.

We are now prepared to adapt M. Regnault's formulas to Eng-
lish measures and our standard thermometer.

Formula (E), which ranges from - 32° C. to o° C., becomes

<-4, + ft,<-*, (EJ

in which

ati = — 0.003 241 802

Log ati = 0.018506945829
Log bft = 1.266914897

* As some typographical errors have N = o, in which
crept into the equations given by M. Reg- A?/i Ay-2-AyoAy.-i

nault ("Mem. de Tlnst., tome xxi. p. 596), (Ayi)~ - Ayo A^ '

for the determination of the constants a, (Ay2)2- Ayt Ay3

and /3 in the formula (AyO* - Ay0 Ay2 '

Log F= a + 6a/ + c/3/, and

we subjoin the correct expressions. « and a = i ^ Log /3 = - log /3.

/3 are the roots of the quadratic z* - Mz + n n

CHAP. II.] EXPLANATION OF FOLLOWING TABLES. 253

In tliis formula T is counted from 32° F., positively, downwu
it ranges from T= o to T= 64, or from 32° F. 10-3: I

Formula (D), which applies between o° and 100 C., becomes

Log t « a, + baj - cfij, 1 > >

where

a,,= 3-335 864 69° 9
Log aH = 0.003 813 443 °7^
Log fif= 1.998 181 052 570
Log bit = 2.131 947611 ooo
Log cu = 0.61 1 742 663 ooo

In this formula, which answers between the limits 32° and 212°
I . '/'denotes the number of Fahr. degrees, counted from"32° po-
M lively, upwards.

Formula (H) becomes

Log * = a, - btiaj - cj3,/7, < 1 1 )

in which

a,, = 4-859 984 524 7
Log a, = ^.9990797513

L°g ft, = '-996 6937?8 3
Log £, = 0.659 317 975 2
Log ca = 0.020 5174324

presents degrees Fahr., counted from 32° F., and this for-
mula IKIS been employed between the limits 212° and 432°.

A break will be observed in the continuity of the first ami s--
1 tables at the pressure corresponding to 32°; this is owin
• •iivum.-taiuv that the curve n 1 l>y formula (D i

t he curve represented by (E) at u sensible tli / Mnall n

In t '1 and thinl tal«K-.^ tin- j.r.^suivs fnrn'sjumd:'

whole decrees were calculated from the formula' ; tin- valm
tin- iiit«-nii«:«liat«' i'racti-nal JM. :ncd Iroin the formula

of interpolation,*

in which h i, //' = o.i, o.2, 0.3, &c., and du, A A

first, M'cond, and third diHrrrnceS.

i ; i • I ' ' I, In Tabl« 1 V

254 EXPLANATION OF FOLLOWING TABLES. [BOOK I.

given the values of (i -f n sin2 X), and also of its reciprocal for
every five degrees of latitude from the equator to the pole, by
means of which the length of a column of mercury at the equator
equivalent to a given column at any latitude, and vice versa,
may be readily found with a degree of accuracy sufficient for
most cases.

In Table V. we have given the values of the absolute dilata-
tion of mercury, and of its mean coefficient for i° F. for every
twenty degrees of our standard thermometer. This table has
been calculated from the formula in p. 70, which, being adapted
to our thermometer, becomes

where Tis the temperature in degrees Fahr., counted from 32°,

and

Log ati — 5.997 550 7 a/t = o.ooo 099 437 6

Log bu = 9.891 307 5 bu = o.ooo ooo 007 785 88

This table is useful for reducing the length of the mercurial
column at any temperature to its equivalent at 32° F. For this
purpose it is necessary to substitute in the expression

the value of 8, as given in the third column of the table, for the
temperature nearest to T. If extreme accuracy is required, the
value corresponding to any temperature T is easily obtained by
interpolation, on the supposition that the rate of increase of the
mean coefficient is uniform for each interval of 20°.

In all reductions of the height of the barometric column, we
may safely take for 8 the value corresponding to 60° F. This
value, reduced to the form of a vulgar fraction, is i -r- 10034.5 ;
substituting this in the expression for //,, and solving for Y/^,
we obtain

// n IO°34-5

J/< 10034.5 + <r-3*)

Table VI. contains the mean coefficient of dilatation for i°
Fahr., from 32° to 652° F., of flint and crown glass, calculated
from the formula; given by M. Regnault, which, when adapted
to our thermometer, are

(HAP. II.] I ANA! ION OF FOLLOWING TABLES. 255

For Flint <J( For Crown <,

log b= 5.0988536 log b = 5.161 874 5

log c = "10.863 499 3 ^0 = 9.6585134

in which kr is the absolute dilatation from 32° to Ty and 7' i<
counted from 32°.

Table VII. is taken from M. Regnaults memoir, and exhibit*
a comparison of the indications of an air thermometer corrected
for the expansion of its envelope, and of mercurial thermometers
constructed with four diil'erent kinds of glass, namely, French
crystal, a double silicate of potash and oxide of lead, similar to
ouTjlinf a double silicate of lime and potash,

or soda, analogous to our crown <jla**; verre vert, a multiple sili-
cate of lime, oxide of iron, alumina, and potash or soda, corres-
ponding to the common bottle glass; and lastly, a kind of very
in fusible glass, of which M. Regnault obtained some specimens
from Sweden.

In Table VIII. we have Driven tin- absolute densities of va-
rious simple and compound gaseous bodies, as determined by
direct experiment. It is usual to introduce into tables of this-
kind a column exhibiting the / .'. --n>ity of such bodies, de-

•d from Gay-Lussac's law of volumes, but we have thought it
replace this column by one showing the relation
the volumes of compounds and those of their element-.
- ol'tliis column the .student will be able to calculate,
either tin- theoretic density of a compound fn.ni the experimen-
tal densities of its elements, «n- the theoretic den>ity ofonc element
from the experimental <lt pound and the «•:

element, or linally, if the -ame common element enter- into
rious combinations, to the dii:

it- t ity, according as \ one or oth-M

compounds.

• In M. Kegnmult's memoir, instead of gi mrmnir f..r *

tin- f..riniil:i f..r ili- a1 \c« valu^ lc-M than Uioac awi^i !

Hint glatt, the formula, appar< i Bcgnault, below 2 1 2 , uhi<iii

nt .lil.ii.iti..ii ,,f in, :,'.i\ in th.it mi ••: latli> consequence, an

•,nla in hi^lirr i
lurrd fp-ii '

250 EXPLANATION OF FOLLOWING TABLES. [BOOK I.

Table IX. contains the weights, in English grains, of 100
cubic inches of air and four other gases, whose densities have been
determined by M. Regnault with extreme accuracy. In the third
column is given the weight of this volume under the pressure of
thirty inches at the equator ; in the fourth the weight of the same
volume under the pressure of a column of mercury of the same
height at Dublin. The temperature of the gas is supposed to be
the same in both cases, namely, that of melting ice.

The weight of the same volume of any of those substances at
32°, and under a pressure of thirty inches of mercury at any la-
titude, may be obtained by multiplying the number in the third
column by (i + n sin2 X), or with sufficient accuracy in most cases,
by the value in Table IV., corresponding to the latitude nearest
to that of the place of observation.

These weights were calculated as follows:

M. Regnault has ascertained that a litre of dry air at o°, and
under the pressure produced by 760"™ of mercury at the Obser-
vatory of Paris, weighs 1^.293 I^7- Now those 760""" are equi-.
valent to 762mm.2796, at the sea level under the equator, while
thirty inches are only equal to 76imm.9862 ; the preceding weight,

therefore, must be reduced in the ratio ^—r-— ^ in order to ob-

762 279 6

tain the weight of the litre of air at o° 0., under a pressure of
thirty inches at the equator. This gives the weight equal to
1^.292689.

Now ilil = 61.027 °5 English inches, and i gramme = 15.433
English grains; and hence we obtain, finally, the weight of 100
cubic inches of dry air at the temperature of melting ice, and
under the pressure of thirty inches of mercury at 32° F. at the
sea level under the equator, equal to 32^.690 541.

At Dublin, under the pressure of a column of the same height,
the weight equals 32grs.8o2 342.

Having thus obtained the weight of 100 cubic inches of dry
air, the weights of the same volume of the other substances enu-
merated in the table are obtained by multiplying the preceding
weights by the respective absolute densities.

Table X. exhibits the elastic forces of the vapours of various
liquids, according to the best authorities.

.HAP. II.]

ELASTIC FORCE OF AQUEOUS VAPOUR.

257

TAELE I.

TABLE of the elastic Force of aqueous Vapour from - 30° to 432°

Fahr.

Tempe-
rature.

at S-

.Mm. at ;
Sea Level ut Dul,-
lin (I.

Tempe-
rature,

Force in Inches of
tiry at 32°,
at Sea Level at

!•'.'! nator.

Force in Inches of
Merc, at 32", at
Sea Level at Dub-

lin(l

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at

Ivi u

Force iii In
i \ at
BaaLmlal

lin(Lat. 53° 21').

-30°

o'.oo99

0^0099

+ 6°

0^0578

0^0576

40°

o'.2483

ol-2475

29

0.0105

0.0105

7

o .0605

0.0603

4'

0.2580

0.2571

28

O.OIII

O.OIII

8

0.0632

0.0630

42

0.2681

0.2672

27

0.0117

O.OII7

9

0.066 1

0.0659

43

0.2785

0.2775

26

0.0124

0.0123

10

0.0692

0.0689

44

0.2892

0.2882

25

0.0131

O.OI3O

ii

0.0723

0.0721

45

0.3003

0.2993

24

0.0138

0.0137

12

0.0756

0.0753

46

0.3118

0.3108

23

0.0145

0.0144

13

0.0790

0.0788

47

0-3237

0.3226

22

0.0153

o 0152

'4

0.0826

0.0823

48

0.3360

0.3349

21

0.0161

0.0160

15

o .0864

0.0861

49

0.3487

0.3476

20

o .0169

0.0168

16

o .0903

0.0899

5°

0.3619

0.3607

0.0178

0.0177

17

0.0943

0.0940

51

0-3755

0.3742

18

0.0187

0.0186

18

0.0986

0.0982

52

0.3895

0.3882

17

0.0197

0.0196

19

0.1030

0.1027

53

o .4040

0.4026

16

0.0207

0.0206

20

0.1076

0.1073

54

0.4189

0.4175

'5

0.0217

0.0216

21

0.1125

O.I 121

55

0-4344

0.4329

*4

3.0228

0.0227

22

0.1175

O.II7I

56

0.4504

o 4488

'3

0.0239

0.0238

23

0.1228

0.1223

57

o .4668

0.4653

12

0.0251

0.0250

24

0.1282

0.1278

58

0.4839

0.4822

I I

0.0263

0.0262

25

0.1340

0.1335

I9

0.5014

0-4997

10

0.0276

0.0275

26

0.1399

0.1395

60

0.5195

0.5178

o .0290

0.0289

27

0.1462

0.1457

61

0.5382

0.5364

o .0304

o .0303

28

0.1527

62

>56

7

o .03 1 8

0.0317

29

0.1595

O.I589

*3

°-5755

6

0-0334

0.0332

30

0 . 1 660

64

0.5980

0.5959

5

4

0.0350
o .0366

0.0348
0.0365

3'

32

0 . I S I 0

0.1810

65
66

0.0191

0.6170
0.6388

3 |o-o384

0.0382

67

0.6635

0.6612

2

o .0402

0.0400

32°

0.1816

o.iSio

68

o .6867

o .6843

I

o .042 1

0.0419

33

o . 1 890

0.1883

69

0.7106

0.7081

O

o .0440

0.0439

o . 1 966

70

0.7327

+ I

0.0461

0.0459

35

0.2045

0.2038

7'

0.7580

2

0.0482

o .048 1

0.21 19

0.7868

0.7841

3

0.0505

o .0503

37

0.221 I

0.2204

73

0.8109

4

0.0528

0.0526

38

0.2291

74

0.8415

0.8386

5

0.0553

0.0551

39

0.2389

0.2381

75

0.8701

0.8671

2 L

258

TABLE I.

[BOOK I.

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at
Equator.

Force in Inches of
Merc, at 32°, at
Sea Level at Dub-
lin (Lat. 53° 21').

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at
Equator.

Force in Inches of
Merc, at 32°, at
Sea Level at Dub-
lin (Lat. 53' 21').

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at

Kquator.

Force in Inches of
Merc, at 32°, at
Sea Level at Dub-
lin (Lat. 53° 21').

76°

0^8995

0^8964

121°

3'-532

3i-520

1 66°

I I '.126

I I '.088

77

0.9298

0.9266

122

3.631

3.619

167

11.389

11.350

78

0.9610

°-9577

I23

3-733

3.720

168

11.657

11.617

79

0.9931

0.9898

124

3.837

3.824

169

11.930

11.889

80

.0262

1 .0227

I2|

3-944

3-93°

170

12 .209

12.167

81

.0602

I .0566

126

4.053

4-039

171

12-493

12.450

82

.0952

1.0915

I27

4.164

4.150

172

12.783

'2-739

83

.1312

1.1274

128

4.278

4.264

!73

13.078

1 3-033

84

.1683

1 .1643

I29

4-395

4.381

'74

'3-379

'3-333

85

.2064

1 .2023

I30

4-5'5

4.500

'75

13.686

'3-639

86

.2456

.2413

'31

4.638

4.622

176

13.998

'3-95'

87

.2859

.2815

I32

4-763

4-747

177

H-3'7

14.268

88

•3273

.3228

'33

4.891

4.874

178

14.642

14.592

89

.3699

.3652

'34

5 .022

5.005

179

'4-973

14.922

90

•4137

.4088

J35

5.156

5-J39

1 80

15.310

15.258

91

.4587

•4537

136

5.293

5-275

181

I5-653

1 5 .600

92

.5049

.4998

'37

5-434

5-4'5

182

1 6 .003

15.949

93

.5524

•5471

138

5-577

5-558

183

16.360

16.304

94

.6012

.5958

'39

5.724

5-7°4

184

16.723

16.666

95

.6514

.6457

140

5.874

5.854

185

17.093

'7 -°34

96

.7029

.6971

141

6.027

6.006

186

17.469

17.410

97

•7558

.7498

142

6.183

6.162

187

I7-853

17.792

98

.8101

.8039

'43

6- 343

6.322

188

18.243

18.181

99

1.8658

.8595

144

6.507

6.485

189

18.641

18.577

100

1.923

.917

H5

6.674

6.651

190

1 9 .046

18.981

101

i .982

•975

146

6.845

6.822

191

19.458

19.392

102

2.042

2.035

'47

7.019

6.996

192

19.878

19.810

103

2.104

2.097

148

7.198

7-J73

'93

20.305

20.236

IO4

2.168

2.160

149

7.38o

7-354

194

20.740

20.669

IO5

2-233

2.225

150

7.566

7-54°

'95

21.182

21 .IIO

1 06

2.300

2 .292

'51

7.756

7.729

196

21 .632

21.559

107

2.368

2.360

152

7-949

7.922

197

22 .091

22 ,0l6

108

2 -439

2.430

'53

8.147

8.120

198

22.557

22 .480

.109

2.511

2 .502

J54

8-349

8 .321

199

23.032

22.953

I 10

2.585

2.576

'55

8.556

8.527

200

23-5'5

23435

1 1 1

2.661

2.652

156

8.767

8.737

201

24 .006

23.924

112

2 -739

2.729

'57

8.982

8.951

202

24.506

24.422

I'3

2.818

2.809

158

9.201

9.170

203

25.014

24.929

114

2 .900

2.890

'59

9.425

9.393

204

25-532

25.445

"5

2.984

2.974

1 60

9.654

9.621

205

26.058

25.969

116

3.070

3.059

161

9.887

9.853

206

26.593

26.502

117

3.158

3-H7

162

10.125

10.090

207

27.137

27.045

118

3-H8

3-237

163

10.368

10.332 j

208

27.691

27.597

119

3.340

3.329

164

10.616

10.579

2O9

28.254

28.158

120

3-435

3-423

16;

10.868

10.831

210

28.826

28.728

CHAP. II.]

ELASTIC FORCE OF AQUEOUS VAPOUR.

Tempe-
rature.

nog

1*ic

Tempe-
rature.

Force in Iii.-li.-.sof
it 32°,
> a Level at
Equator.

Seal.

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at
Equator.

:

iry 32°, at
lin(Lat.53>2i').

211°

29'.4o8

29^.308

256°

67'.66

67'43

301°

139^26

'38V79

212

30 .000

29.898

257

68.84

68.60

302

141 .36

140.88

213

30.60

30.50

258

70.02

69.79

3°3

143.48

142.99

214

31.21

3'. 'i

259

7'« 23

70.99

304

I45-63

I45-'3

3' -83

3'. 73

260

72.45

72.20

305

147.80

'47 .3°

216

32.46

32.35

261

73-69

73-44

306

150.00

149.49

217

33-"

32.99

262

74-94

74.69

307

152 .22

151.70

218

33.76 33.64

263

76.22

75.96

308

' 54 -47

'53-95

219

34.42 34.30

264

77-5'

77.24

309

156.75

156.22

220

35-09

34.98

265

78.81

78-55

3'0

159.05

158.51

221

35-78

35.66

266

80.14

79.87

3"

161 .38

160.83

222

36-47

267

8 1 .48

81.21

3'2

'63-74

163.18

223

37-'8

37.05

268

82.85

82.56

166.13

165.56

224

37-90

37 -77

269

84.23

83.94

3'4

168.54

167.97

38.63

38.50

270

85-63

85.33

170.98

170.40

226

39-37

39.23

271

87.04

86-75

316

'73-45

172.86

227

40.12

39.98

272

88.48

88.18

3'7

'75-95

'75-35

228

40.88

40.74

273

89.94

89.63

318

178.47

177.86

229

41.66

41.52

274

91 .A I

91 .10

3'9

iSi .02

180.41

230

42 .45

42.30

275

92.91

92.59

320

183.61

182.98

23'

43-25

43-'o

276

94 .42

94.10

321

186.22

185.59

232

44.06

43-9'

277

95.96

95.63

322

188.86

188.22

233

44.89

44-73

278

97-5'

97- '8

323

'9'. 53

190.88

234

45.72

45-57

279

99-09

98.75

324

194-23

'93-57

235

46.57

46.42

280

100.68

100.34

325

196.96

196.29

236

47-44

47-28

281

IO2 .30

101.95

326

'99-73

199.05

237

48.31

48.15

282

'03.93

103.58

327

202 .52

238

49.20

49.04

283

105.59

105.23

328

205.34

204.64

239

50.11

49-94

284

106.91

329 20^.20

207 .49

240

51 .02

285

108.97

108.60

330

21 I .08

210.36

24I

5' -95

286

1 10.69

1 10.32

33'

214.00

242

52.90

287

112.44

112.05 332

216.95

216.21

243

53-86

53-67

2X8

114.20

"3.8i

333

219.93

219.18

244

54.83

54.64

789

1 1 5 .99

1 1 5 .60

334

222 .18

55.82
56.82

55-63
56.62

290
291

117.80
119.64

117.40

335
336

225.98
229.06

228.28

247

57 -83

57.64

292

121.49

I 2 I .08

337

231.38

248

58.87

58.66

293

'23-37

338

235-5'

59.91

59-7'

125.27

124.85

339

238.49

237.68

250

60.97

60.76

295

127.20

126.77

340

240.88

62.05

296

129.15

128.71

H4.95

252

63. ,4

62.92

297

i ;o 68

247.38

253

64.03

298

'32.67

250.69

65.37

299

'34-68

344

254.89 254.02

255

66.51

66.28

300

258-27 257.39

260

TABLE I.

[BOOK i.

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at
Equator.

Force in Inches of
Merc, at 32°, at
Sea Level at Dub-
lin (Lat. 53 21').

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at
Equator.

Force in Inches of
Merc, at 3 2°, at
Sea Level at Dub-
lin (Lat. 53° 2i>

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at
Equator.

Force in In. hes of
Merc, at 32% at
Sea Level at Dub-
lin (Lat. 53° 21').

3460

26 1 '.69

26oi.8o

375°

377^26

375'-98

404°

528^93

527'.I2

347

265.15

264.24

376

381.86

380.55

405

534-88

533.06

348

268 .64

267.72

377

386.49

385.17

406

540.88

539-04

349

272.16

271.23 !

378

39I-I7

389.84

407

546 -94

545 -°7

35°

275.72

274.78

379

395-89

394-54

408

553-04

551.16

351

279.32

278-37

380

400 .66

399.29

409

559-20

557.30

352

282.96

281.99

38i

405 .47

404 .09

410

565.41

563 .48

353

286.63

285.65

382

410.32

408 .92

411

571.67

569«73

354

290.34

289.35

383

415.22

413-81

412

577-99

576.02

355

294.08

293 .08

384

420.17

418.73

4'3

584.36

582.36

356

297.87

296.85

385

425.16

423 -71

414

590.78

588.76

357

301 .69

300 .66

386

430.19

428.73

4'5

597-25

595.22

358

3°5'55

304 -5 '

387

435.27

433 -79

416

603 .78

601 .72

359

309.45

308.39

388

440.40

438.90

4'7

610.36

608.28

360

3U.38

312.32

389

445.57

444 .06

418

617 .00

614.90

361

3'7-36

316.28

390

450.79

449.26

419

623 .69

621 .56

362

321.38

320.28

39'

456.06

454- 51

420

630 .44

628.29

363

325.43

324-32

392

461 .38

459.80

421

637.24

635-°7

364

329.53

328 .40

393

466 .74

465.15

422

644.09

641 .90

365

333.66

332.52

394

472.15

470.54

423

651 .01

648 .79

366

337-83

336.68

395

477 -60

475.98

424

657-97

655-73

367

342 -05

340.88

396

483.11

481 .46

425

665.00 662.73

368

346.31

345 -'3

397

488 .66

487.00

426

672 .08

669.79

369

350.60

34941

398

494.27

492.58

427

679 .22

676.90

37°

354-94

353-73

399

499 .92

498 .22

428

686.41

684.07

371

359-32

358.10

400

505 .62

503 .90

429

693 .66

691 .30

372

363 -74

362.50

401

5II-37

509 .63

43°

700.97

698.58

373

368.21

366.95

402

517.17

5 '5 -4-1

43i

708.34

7°5 -92

374

372.71

37 '-44

403

523.02

521.24

432

715.76

7x3-32

CHAP. II.]

ELASTIC FORCE OF AQUEOUS VAPOUR.

26l

TABLE II.

TABLE of the elastic Force of aqueous Vapour from o° to 100° F.
for every tenth of a Degree.

Tempe-
rature.

ury at 32 ,
at Sea Level at

Kquator.

in Inches of
Merc, at 32°, at
Sea Level at Dub-
lin (Lat 53° 2O.

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at
Equator.

Force in Inches of
Merc, at 32°, at
Sea Level at Dub-
lin (Lat. 53 21').

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at
Equator.

Force in Inches of
. at 32°, at
Sea Level at Dub-
lin (Lat 53° 2i>

o°.o

oi.0440

0^0439

3'.6

©'.05 1 9

o'.o5i7 1

7°-*

0^06 10

0^0608

.1

0.0442

0.0441

•7

0.0521

0.0519

•3

0.0613

O.o6 1 1

.2

0.0444

0.0443

.8

0.0524

0.0522

•4

0.06 1 6

0.0614

•3

o .0446

0.0445

•9

0.0526

0.0524

•5

0.06 1 8

0.06 1 6

•4

0.0449

0.0447

4.0

0.0528

0.0526

.6

0.0621

0.0619

•5

0.0451

0.0449

.1

0.0531

0.0529

•7

0.0624

0.0622

.6

0.0453

0.0451

.2

0-0533

0.0531

.8

0.0627

0.0625

•7

0.0455

0-0453

•3

0.0535

0-0534

•9

0.0630

0.0627

.8

0.0457

0.0455

•4

0.0538

0.0536

8.0

0.0632

0.0630

•9

0.0459

0.0457

•5

0.0540

0.0539

.1

0.0635

0.0633

I .0

o .046 1

0.0459

.6

0.0543

0.0541

.2

0.0638

0.0636

.1

o .0463

0.0462

.7

0.0545

0.0543

-3

o .064 1

0.0639

.2

0.0465

0.0464

.8

0.0548

0.0546

•4

0.0644

0.0642

•3

0.0467

o .0466

•9

0.0550

0.0548

•5

0.0647

0.0645

•4

o .0469

o .0468

5-°

0.0553

0.0551

.6

0.0650

0.0647

•5

0.0472

o .0470

.1

0.0555

0.0553

•7

0.0653

0.0650

.6

0.0474

0.0472

.2

0.0558

0.0556

.8

0.0656

0.0653

•7

0.0476

0.0474

•3

0.0560

0.0558

•9

0.0658

0.0656

.8

0.0478

0.0476

•4

0.0563

0.0561

9 -o

o .066 1

0.0659

•9

o .0480

0.0479

.J

0.0565

0.0563

.1

o .0664

0.0662

2 .0

0.0482

0.0481

.6

0.0568

0.0566

.2

0.0667

0.0665

.1

0.0485

0.0483

•7

0.0570

0.0568

•3

0.0670

0.0668

.2

0.0487

o .048 5

.8

0.0573

0-0571

•4

0.0673

0.0671

•3

o .0489

0.0487

•9

0.0576

0-0574

.!

0.0676

0.0674

•4

o .049 1

o .0490

6.0

0.052*

0-0576

.6

0.0679

0.0494

0.0492

.1

0.0581

0-0579

0.0682

0.0680

.6

o .0496

0.0494

.2

0-0583

0-0581

.8

0.0685

0.0683

•7

o .0498

o .0496

•3

0-0586

0-0584

•9

0*0689

cr.o686

.8

0.0500

0.0499

•4

0.0589

0-0587

10 .0

0.0692

0.0689

•9

0.0503

0.0501

0.0591

0-0589

.1

0.0695

0.0692

3-0

0.0505

0.0503

0.0594

0-0592

.2

o .0698

0.0695

.1

0.0507

0.0505

•7

0.0597

0-0595

•3

0.0701

0.0698

.2

0.0509

0.0508

.8

0.0597

•4

0.0704

0.0702

•3

0.0512

0.0510

•9

0.0602

0.0600

0.0707

0.0705

•4

0.0514

0.0512

7 -°

0.0605

0.0603

.6

0.0710

0.0708

•5

0.0516

0.05.5

0.0607

0.0605

•7

0.0714

0.071 1

262

TABLE II.

[BOOK

Tempe-
rature.

Force in Inches of
Mercury at 32 ,
at Sea Level at
Equator.

Force in Inches of
Merc, at 32°, at
Sea Level at Dub-
lin (Lat. 53 21').

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at

Equator.

Force in Inches of
Merc, at 32°, at
Sea Level at Dub-
lin (Lat. 53° 2 11).

Tempe-
rature.

°°~13

I"!.

« tJ > o

C * <V -S

Jill

IS*

Force in Inches of
Merc, at 32 , at
Sea Level at I hi! -
lin(Lat. 53^21').

I0°.8

o'.o7i7

0^0714

'5°-3

0^0875

0^0872

I9°.8

os. 1 06 7

0J.I063

•9

0.0720

0.0717

•4

0.0879

0.0876

•9

0.1072

0.1068

1 1 .O

0.0723

0.0721

•5

0.0883

O.o88o

20 .O

0.1076

0.1073

.1

0.0726

0.0724

.6

0.0887

0.0884

.1

0.1081

0.1077

.2

0.0730

0.0727

•7

0.0891

O.o888

.2

0.1086

0.1082

•3

0.0733

0.0730

.8

0.0895

0.0892

•3

0.1091

0.1087

•4

0.0736

0.0734

•9

0.0899

0.0896

•4

0.1095

0.1092

•5

0.0739

0.0737

1 6 .0

0.0903

0.0899

•5

O.I IOO

0.1096

.6

0.0743

0.0740

.1

0.0907

0.0903

.6

o.i 105

O.I IOI

•7

0.0746

0.0743

.2

0.091 I

0.0907

•7

O.I I 10

0.1106

.8

0.0749

0.0747

•3

0.0915

0.091 I

.8

0.1115

O.I III

•9

0.0753

0.0750

•4

0.0919

0.0916

•9

O.I I2O

o . i ii 6

12 .0

0.0756

0-0753

•5

0.0923

0.0920

21 .0

o.i 125

O.I 121

.1

0.0759

0.0757

.6

0.0927

0.0924

.1

o.i 130

o.i 126

.2

0.0763

0.0760

•7

0.0931

0.0928

.2

0.1134

o.i 131

-3

0.0766

0.0764

.8

0.0935

0.0932

•3

0.1139

o.i 136

•4

0.0770

0.0767

•9

0.0939

0.0936

•4

0.1144

0.1141

•5

0.0773

0.0770

17 .0

o .0943

o .0940

•5

o-i 150

0.1146

.6

0.0776

0.0774

.1

0.0947

0.0944 '

.6

0-1155

0.1151

•7

0.0780

0.0777

.2

0.0952

0.0948

•7

O.I 1 60

0.1156

.8

0.0783

0.0781

•3

0.0956

0.0953

.8

0.1165

0.1161

•9

0.0787

0.0784

•4

0.0960

0.0957

•9

0.1170

o . 1 1 66

13 .0

0.0790

0.0788

•5

o .0964

0.0961

22 .0

0.1175

0.1171

.1

0.0794

0.0791

.6

0.0969

0.0965

.1

O.I I 80

0.1176

.2

0.0797

0.0795

•7

0.0973

0.0969

.2

0.1185

0.1181

-3

0.0801

0.0798

.8

0.0977

0.0974

•3

o.i 190

0.1186

•4

0.0805

0.0802

•9

0.0981

0.0978

•4

0.1196

o.i 192

•5

0.0808

0.0805

1 8 .0

0.0986

0.0982

• 5

O.I2OI

0.1197

.6

0.0812

0.0809

.1

0.0990

0.0987 I

.6

o.i 206

O.I2O2

.7

0.0815

0.08 I 2

.2

0.0994

0.0991 j

•7

0-1112

0.1207

.8

0.0819

0.08 1 6

•3

0.0999

0.0995 1

.8

O.I2I7

O.I2I3

•9

0.0823

0.0820

•4

0.1003

O.IOOO

•9

O.I222

0.1218

14.0

0.0826

0.0823

•5

o.i 008

0.1004

23 .0

0.1228

0.1223

.1

0-0830

0.0827

.6

O.IOI2

o . 1 009

.1

0.1233

O.I229

.2

0.0834

0.0831

•7

O.IOI7

0.1013

.2

0.1238

0.1234

•3

0.0837

0.0834

.8

O.I02I

0.1018

•3

0.1244

0.1239

•4

0.0841

0.0838

•9

O.IO26

O.IO22

.4

0.1249

0.1245

•5

0.0845

0.0842

19 .0

O.IO3O

O.IO27

•5

0.1255

0.1250

.6

0.0848

0.0846

.1

0.1035

0.1031

.6

O.I26O

0.1256

.7

0.0852-

0.0849

.2

O.IO39

0.1036

•7

O.I266

O.I26l

.8

0.0856

0.0853

•3

o . 1 044

o . 1 040

.8

0.1271

0.1267

•9

0.0860

0.0857

•4

o . 1 048

0.1045

•9

0.1277

0.1272

15 .0

0.0864

0.0861

•5

0.1053

0.1049

24.0

0.1282

0.1278

.1

0.0867

0.0864

.6

0.1058

0.1054

0.1288

0.1284

.2

0.0871

0.0868

•7

0.1062

0.1059

.2

0.1294

0.1289

CHAP. II.]

ELASTIC FORCE OF AQUEOUS VAPOUR.

263

Tempe-
rature.

Force in In. '

TV ;it 32 ,

at Sea 'Level at

K<|u

Force iii In
Merc, at 3 .
Sea Level at Hul.-

lind.at. 53

Tempe-
rature,

Force in Inches of

at Sea Level at

F.<|iiator.

Force in In
Merc, at 3
Seal.'

li.XLat.53 21').

Tempe-
rature.

Forcoin In.
Mercury at 32 ,
at Sea Level at
l.ijiiator.

Force in Inches of
M. re, at 32 , at
Sea Level at Dub-
lin (Lat 53° 21').

0

©'.1299

0-.I295

28°.8

0^158 1

°i-I575

33°-3

O1. 1 9 1 2

0^1906

•4

0.1305

0.1300

•9

0.1588

0.1582

•4

0.1920

0.1913

•5

O.I3II

0.1306

29 .0

0.1595

0.1589

•5

0.1928

0.1921

.6

0.1317

0.1312

.1

o.i 602

0.1596

.6

°-I935

0.1929

•I

0.1322
0.1328

0.1318
0.1323

.2

•3

0.1609

0.1616

0.1603
0.1610

•1

0.1943
0.1951

0-1936
0.1944

•9

0.1334

0.1329

•4

0.1623

0.1617

•9

0.1958

0.1952

25 .0

0.1340

°-'335

•5

0.1630

0.1624

0.1966

0.1959

0.1345

0.1341

.6

0.1637

0.1631

• I

0.1974

0.1967

.2

0.1351

°-I347

•7

0.1644

0.1638

.2

0.1982

0.1975

•3

0.1357

0-1353

.8

0.1651

0.1645

•3

0.1989

0.1983

.4

0.1363

0.1359

•9

0.1658

0.1653

•4

0.1997

0.1990

.5

0.1369

0.1364

30 .0

0.1665

o.i 660

0.2005

0.1998

.6

0.1375

0.1370

.1

0.1673

0.1667

.6

0.2013

0.2006

•I

0.1381
0.1387

0.1376
0-1382

.2
•3

0.1680
0.1687

0.1674
0.1682

•I

0.2021
0.2029

0.2014

0.2022

•9

0.1393

0.1388

•4

0.1695

0.1689

•9

0.2037

0.2O3O

26 .0

0.1399

o 1395

•5

0.1702

0.1696

35 -°

0.2045

0.2038

.1

0.1405

0.1401

.6

0.1709

0.1704

0.2053

0.2046

.2

0.14.2

0.1407

•7

0.1717

0.171 1

.2

0.2O6 I

0.2054

•3

0.14.8

0.1413

.8

0.1724

0.1718

•3

0.2069

0.2062

•4

0.1424

0.1419

•9

0.1732

0.1726

•4

0.2077

0.2070

• 5

0.1430

0.1425

31 .0

0.1739

o.i733

0.2085

0.2078

.6

0.1436

0.1431

.1

0.1747

0.1741

.6

0.2094

0.2086

•7

0.1443 0.1438

.2

0.1755

0.1749

•7

O.2I02

0.2095

.8

0.1449 0.1444

•3

0.1762

0.1756

.8

O.2I IO

0.2103

•9

0.1455 0.1450

.4

0.1770

0.1764

•9

0.21 l8

0.21 I I

27 .0

l 0.1457

.5 0.1777

0.1771

36 .0

0.2127

0.21 19

..

0.1468 o.

.6 0.1785

0.1779

.1

.2

0.14

0.1469

•7 0.1793

0.1787

.2

0.2.43

.3

0.1481

.8 0.1801

0.1795

•3

•4

0-1487

.9 0.1809

0.1802

•4

•i

0.1494

o.i 500

0.1495

32 .0 0.1816
.1 0.1824

o . i 8 i o

0.2168
0.2177

•I

0.1507
0.1513

0.1502
0-1508

.2 0.1831
.3 0.1838

0.1825
0.1832

•I

0.2185

•9

o-i 520 0-15.5

.4 0.1846

0.1839

•9

0.2202

28 -o

0.1853

0.1847

37.0

0.221 I

O.22O4

..

o.i;

0 . 1 860

• i

.2

rO

0.1868

0.1861

.2

0.2228

O.222I

0.1547 o,

.8 0.1875

0.1869

0.2229

.9 0.1882

0.1876

•4

0.2238

3 0.1555

33 .0 0.1890

0.1883

.6

.. 0.1897

0.1891

.6

0.1574

.2 0.1905

0.1898

•7

0.2264

264

TABLE II.

[BOOK i.

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at
Equator.

Force in Inches of
Merc, at 32°, at
Sea Level at Dub-
lin (Lat. 53° 21').

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at
Equator.

Force in Inches of
Merc, at 32°, at
Sea Level at Dub-
lin (Lat. 53° 21').

Tempe-
rature.

Force in Inches of
Mercury at 32 ,
at Sea Level at
Equator.

Force in Inches of
Merc, at 3 2°, at
Sea Level at Dub-
lin (Lat 53C 21').

37°-8

O!.228l

0'.2273

42°-3

0^2712

0^2702

46°.8

0^3213

O!.3202

o'9

0.2290

0.2282

•4

0.2722

0.2713

•9

0.3225

0.3214

38 .0

0.2299

0.2291

•5

0.2732

0.2723

47 -°

0-3237

0.3226

• i

0.2308

0.2300

.6

0.2743

0-2733

.1

0.3250

0.3238

.2

0.2317

0.2309

.7

0-2753

0.2744

.2

0.3262

0.3251

•3

0.2326

0.2318

.8

0.2764

°-2754.

•3

0.3274

0.3263

•4

0-2335

0.2327

•9

0.2774

0.2765

•4

0.3286

°-3275

•5

0.2344

0.2336

43 -o

0.2785

0.2775

•5

0.3298

0.3287

.6

0.2353

0.2345

.1

0.2795

0.2786

.6

0-3311

0.3299

•7

0.2362

0.2354

.2

0.2806

0.2796

•7

0.3323

o-3312

.8

0.2371

0.2363

•3

0.2817

0.2807

.8

0-3335

0.33H

•9

0.2380

0.2372

•4

0.2827

0.2818

•9

0.3348

0.3336

39-o

0.2389

0.2381

•5

0.2838

0.2828

48 .0

0.3360

0-3349

.1

0.2399

0.2390

.6

0.2849

0.2839

.1

0-3373

0.3361

.2

0.2408

0.2400

•7

0.2860

0.2850

.2

0.3385

0.3374

•3

0.2417

0.2409

.8

0-2870

0.2861

•3

0-3398

0.3386

•4

0.2426

0.2418

•9

0-2881

0.2871

•4

0.3411

0-3399

•5

0.2436

0.2427

44.0

0.2892

0.2882

•5

0-3423

0.3412

.6

0.2445

0.2437

.1

0.2903

0.2893

.6

0-3436

0.3424

•7

0.2455

0.2446

.2

0.2914

0.2904

.7

0-3449

0-3437

•8

0.2464

0.2456

•3

0.2925

0.2915

.8

0.3462

0.3450

•9

0.2474

0.2465

•4

0.2936

0.2926

•9

0-3475

°-3463

40 .0

0.2483

0.2475

•5

0.2947

0.2937

49 .0

0.3487

0.3476

.1

0.2493

0.2484

.6

0.2958

0.2948

0.3500

0.3488

• 2

0-2502

0.2494

•7

0.2970

0.2960

.2

°-35I3

0.3501

•3

0.2512

0.2503

•8

0.2981

0.2971

•3

0.3526

o-SSM-

•4

0.2522

0.2513

•9

0.2992

0.2982

•4

0.3540

°-3527

•5

0.2531

0.2523

45 .0

0.3003

0.2993

•5

0-3553

0-3541

.6

0.2541

0.2532

• i

0.3015

0.3004

.6

0.3566

0-3554

•7

0.2551

0.2542

• 2

0.3026

0.3016

•7

0-3579

0.3567

.8

0-2561

0.2552

•3

0.3038

0.3027

.8

0.3592

0.3580

•9

0.2570

0.2562

•4

0.3049

0.3039

•9

0.3606

0-3593

41 .0

0.2580

0.2571

•5

0.3060

0.3050

50 .0

0.3619

0.3607

• i

0.2590

0.2581

.6

0.3072

0.3061

.1

o 3632

0.3620

.2

0.2600

0.2591

•7

0.3084

0.3073

.2

0.3646

0.3633

•3

0.2610

0-2601

.8

0.3095

0.3085

•3

0.3659

0.3647

•4

0.2620

0.2611

•9

0.3107

0.3096

•4

0.3673

0.3660

•5

0.2630

0.2621

46 .0

0.3118

0.3108

•5

0.3686

0.3674

.6

o .2640

0.2631

.1

0.3130

0.3119

.6

0.3700

0.3687

•7

0.2650

0.2641

.2

0.3H2

0.3*3*

•7

0.37*3

0.3701

.8

0.2660

0.2651

•3

0.3*54

0.3*43

' .8

0.3727

0-37*4

•9

0.2670

0.2661

•4

0.3166

o.3i55

•9

0.3741

0.3728

42 .0

0.2681

0.2672

•5

0.3*77

0.3167

51 .0

o-3755

0.3742

0.2691 0.2682

.6

0.3189

0.3178

.1

0.3768

0.3756

.2

0.2701 0.2692

•7

0.3201

0.3190

.2

0.3782

0.3769

CHAP. II.]

ELASTIC FORCE OF AQUEOUS VAPOUR.

Tempe-
rature.

M'-miry .;•
a! >

Equator.

in Inches of

M. iv. at |
' Dill-

lin(Lat. 53 21 ').

Tempe-
rature.

K*
Jr«-

Ifl*

Force iii l\\' :
Merc, at ^

Vrlat hlll-

lin(Lat. ^ 21').

Tempe-
rature.

Force in Inches of
iry at 32°,
at Sea Level at

K<|imtor.

i Inches of
Merc, at 3 2°, at
Sea Level at Dub-
lin (Lat 53° 21').

5'°-3

oi.3796

o'-3783

55°.8

0^4471

0^4456

6o°.3

ol-525i

o'.5233

-4

0.3810

0.3797

•9

0.4487

0.4472

•4

0.5269

0.5251

•5

0.3824

0.3811

56 .0

0.4504

0.4488

•5

0.5288

0.5270

.6

0.3838

0.3825

.1

0.4520

0.4504

.6

0-5307

0.5289

•7

0.3852

0.3839

.2

0.4536

0.4521

•7

0.5326

0.5307

.8

0.3866

0.3853

•3

0-4553

0-4537

.8

0-5344

0.5326

•9

0.3881

0.3867

•4

0.4569

0-4553

•9

0.5363

0-5345

52.0

0.3895

0.3882

•5

0.4585

0.4570

6 1 .0

0.5382

0.5364

.1

0.3909

0.3896

.6

o .4602

0.4586

. i

0.5401

0.5383

.2

o.3923

0.3910

•7

0.4618

0.4603

.2

0.5420

0.5402

•3

o-3938

0.3924

.8

0.4635

0.4619

.3

0.5440

0.5421

•4

0.3952

0-3939

•9

0.4652

0.4636

•4

0.5459

o 5440

•5

0.3967

0-3953

57 -o

0.4668

0.4653

•5

0.5478

0.5459

.6

0.3981

0.3968

.1

0.4685

0.4669

.6

0.5497

0.5479

•7

0.3996

0.3982

.2

0.4702

0.4686

•7

0.5517

0.5498

.8

0.4010

0-3997

•3

0.4719

0.4703

.8

0-5536

0.5517

•9

0.4025

0.401 1

•4

0.4736

0.4720

«9

0.5556

0-5537

53-0

o .4040

0.4026

•5

0-4753

0-4737

62 .0

o-5575

0.5556

• i

0.4055

o .404 1

.6

0.4770

0-4754

.1

0-5595

0.5576

•2

o .4069

0.4055

•7

0.4787

0.4771

.2

0.5615

0-5595

•3

0.4084

0.4070

.8

o .4804

0.4788

•3

0.5634

s

0.5615

•4

0.4099

0.4085

•9

0.4821

0.4805

•4

0.5654

0-5635

•5

0.4114

0.4100

58 .0

0.4839

0.4822

•5

0.5674

0.5655

.6

0.4129

0.4115

• i

0.4856

0.4839

.6

0.5694

0.5675

•7

0.4144

0.4130

.2

0.4873

0.4857

•7

0.5714

0.5694

•8

0.41; J9

0.4145

•3

0.4891

0.4874

.8

0-5734

0.5714

•9

0.4160

•4

0.4908

0.4891

•9

0-5754

0-5734

54-o

0.41X9

0^175

•5

0.4926

0.4909

63 .0

0-5774

0-5755

• i

0-4205

o .4 1 90

.6

0.4943

0.4926

.1

0.5794

0-5775

• 2

0-4220

0.4206

•7

0.4961

0.4944

.2

0.5815

0 5795

•3

0.4235

0.4221

.8

0.4962

•3

0.5835

0.5815

•4

0410

0.4236

•9

0.4996

0-4979

•4

0.5856

0.5836

•;

0.4266

59.0

0.5014

0.4997

0.5876

0.5856

.6

0.4282

0.4267

0.5032

0.9015

.6

o 5897

0.5877

•7

0.4297

0.4282

.2

0.50^0

0.5033

•7

0.5897

.8

o-43 '3

0.4298

•3

0.5068

0.5051

.8

0.5938

0.5918

•4

0.5086

0.5069

•9

0.5959

0.5938

55 -o

• i

0.4329

i

0.5104

0.5087
0.5105

64.0

.1

0.5980
0.6000

0.5959

.2

•7

.2

0.6021

0.6001

.K

*

0.6022

•4

0.4407

•9

•4

0.6063

0.6043

o 4423

o .4408

60 .0

0.6085

0.6064

.6

0.4439

0.4424

.1

o . 5 1 96

0.6106

0.6085

•7

.2

•7

0.6127

0.6106

266

TABLE II.

[BOOK i.

Tempe-
rature.

Force in Inches of
Mercury at 32,
at Sea Level at

I',«|u.itor.

Force in Inchesof
Merc, at 32°, at
Sea Level at Dub-
lin (Lat. 53° 21").

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at
Equator.

Force in Inches of
Merc, at 32°, at
Sea Level at Dub-
lin (Lat. 53° 21').

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea "Level at

Equator.

Force in Inches of
Merc, at 32°, at
Sea Level at Dub-
lin (Lat. 53° 21').

64°.8

0^6148

0{-6i27

6o°-3

oi-7I79

°'-7I54

73°-8

°'-8359

o'.833o

•9

0.6170

0.6149

•4

0.7203

0.7179

•9

0.8387

0.8358

65 .0

0.6191

0-6170

•5

0-7228

0.7203

74.0

0.8415

0.8386

.1

0.6213

0-6192

.6

0.7253

0.7228

.1

0-8443

0.8414

.2

0.6234

0-6213

•7

0.7277

°-7253 1

.2

0.8471

0.8442

•3

0.6256

0-6235

.8

0-7302

0.7277

•3

0.8500

0.8471

•4

0.6278

0.6256

•9

0.7327

0.7302

•4

0.8528

0.8499

•5

0.6300

0-6278

70 .0

0.7352

0-7327

•5

0.8557

0.8527

.6

0.6321

0-6300

.1

o-7377

°-7352 i

.6

0.8585

0.8556

•7

0-6343

0-6322

.2

0.7402

°-7377 j

•7

0.8614

0.8585

.8

0.6365

0-6344

•3

0.7427

0.7402

.8

0.8643

0.8613

•9

0.6387

0-6366

•4

0-7453

0.7427

•9

0-8672

0.8642

66.0

0.6410

0-6388

•5

0.7478

°-7453

75 -°

0.8701

0.8671

.1

0.6432

0-6410

.6

0.7504

0.7478

.1

0-8730

0.8700

.2

0.6454

0-6432

•7

0.7529

0-7503

.2

0.8759

0.8729

• 3

0.6476

0-6454

.8

0-7555

0.7529

•3

0.8788

0.8758

•4

0.6499

0-6477

•9

0.7580

0-7554

•4

0.8817

0.8787

.5

0.6521

0-6499

71 .0

0.7606

0.7580

•5

0.8847

0.8817

.6

0.6544

0-6521

.1

0.7632

0.7606

.6

0.8876

0.8846

•7

0.6566

0.6544

.2

0.7658

0.7632

-7

0.8906

0.8875

.8

0.6589

0-6567

•3

0.7684

0.7657

.8

0.8935

0.8905

•9

0.6612

0-6589

•4

0.7710

0.7683

•9

0.8965

0.8935

67 .0

0.6635

0-6612

-5

0.7736

0.7709

76 -o

0.8995

0.8964

.1

0.6657

0.6635

.6

0.7762

0.7736

.1

0-9025

0.8994

.2

0.6680

0.6658

•7

0.7788

0-7762

.2

0.9055

0.9024

•3

0.6703

0.6681

.8

0.7815

0-7788

•3

0.9085

0.9054

•4

0.6727

0-6704

•9

0.7841

0-7814

-4

0.9115

0.9084

•5

0.6750

0.6727

72 .0

0.7868

0-7841

•5

0.9145

0.9114

.6

0.6773

0.6750

0.7894

0-7867

.6

0.9176

0.9145

•7

0.6796

0-6773

.2

0.7921

0.7894

•7

o .9206

0.9175

.8

0.6820

0.6796

•3

0.7948

0.7921

.8

0.9237

0.9205

•9

0-6843

0.6820

•4

0.7974

0-7947

•9

0.9267

0.9236

68 .0

0-6867

0-6843

-5

0.8001

0-7974

77.0

0.9298

0.9266

.1

0.6890

0-6867

.6

0-8028

0-8001

0.9329

0.9297

.2

0.6914

0-6890

.7 0-8055

0-8028

.2

0.9360

0.9328

•3

0.6938

0-6914

.8 0-8083

0-8055

•3

0.9391

Q-9359

•4

0-6961

o 6938

•9

0-8110

0-8082

•4

0.9422

0.9390

•5

0-6985

0-6961

73 -°

0-8137

0*8109

•5

0-9453

0.9421

.6

o .7009

0.6985

.1

0-8165

0-8137

.6

0.9484

0.9452

-7

0-7033

0-7009

.2

0.8192

0-8164

•7

0.9516

0.9483

.8

0.7057

0.7033

•3

0-8220

0.8192

.8

0-9547

09515

•9

0.7081

0.7057

•4

0-8247

0.8219

•9

0-9579

0.9546

69 .0

0.7106

0.7081

•5

0-8275

0.8247

78 .0

0.9610

0.9577

.1

0.7130

0.7106

.6

0.8303

0.8274

.1

o .9642

0.9609

.2

0.7154 0.7130

-7 0.8331

0.8302

.2

0.9674

o .964 1

CHAP. II.]

ELASTIC FORCE OF AQUEOUS VAPOUR.

267

Tempe-
rature.

M. n
at Sea Lev, 1 .it
Equator.

Sea Level at I >ul>-

liu(I.;,:. y .-. .

Tempe-
rature.

Force in In.
Mercury at 32 ,
at Sea Level at
Equator.

Force in Inches of

Seal..

lin(l,-it. 53 2.).

Tempe-
rature,

Force in Inches of
ury at 32°,
at Sea Level at
Eqnatob

Force in Inches of

M. iv. at -52 , at
Sea Level ai
lin(Lat, 53 21).

78°.3

0^9706

0'.9673

82°.8

'.1239

'.I 2O I

87°.3

I'.2982

'•2937

•4

0.9738

0.9704

•9

.1276

•I237

•4

.3023

•2979

0.9770

0.9736

83 .0

.1312

.1274

•5

.3064

.3020

.6

0.9802

0.9768

.1

•'349

.1310

.6

.3106

.3061

•7

0.9834

0.9801 |

.2

.1386

•1347

•7

•3H7

•3'03

.8

0.9866

0.9833

• 3

.1422

.1383

.8

.3189

•3144

•9

0.9899

0.9865

•4*

.1459

.1420

•9

•3231

.3186

79.0

°-993'

0.9898

•5

.1496

•1457

88 .0

•3273

.3228

.1

0.9964

0.9930

.6

•'533

.1494

.1

.3315

.3270

.2

0.9997

0.9963

•7

.1571

•'531

.2

•3357

•3312

•3

i .0030

0.9995

.8

.1608

.1568

•3

•3399

•3354

•4

i .0063

I .OO28

.9

.1645

.1606

•4

•3442

•3396

•5

i .0096

I .Oo6l

84.0

.1683

.1643

•5

•3484

.3438

.6

i .0129

I .0094

.1720

.1680

.6

•3527

.3481

3

i .0162
1.0195

I .0127
I .Ol6o

.2

.3

.1758
.1796

.1718
.1756

.*8

•357°
•3613

•3524
.3566

•9

i .0229

I.OI94

.4

.1834

.1794

•9

.3656

.3609

80 .0

i .0262

I .0227

.5

.1872

.1832

89-0

•3699

.3652

.1

i .0296

I .O26O

.6

• 1910

.1870

• i

•3695

.2

1.0329

I -0294

.7

.1948

.1908

• 2

•3785

•3738

•3

i .0363

I -0328

.8

.1987

.1946

•3

.3829

•3782

•4

1 -°397

I -0361

.9

.2025

.1984

•4

•3872

•3825

i

i .043 1
i .0465

1 -0395
I .0429

85.0
.i

.2064
.2103

.2023
.2061

.6

.3916
•3960

.3869
.3912

'1

i .0499

I .0463

.2

.2141

.2100

•7

.4004

•39S6

.8

'•°533

I .0497

• 3

.2180

•2139

.8

.4048

.4000

81.0

i .0568
i .0602

I .0566

•4
• 5

.2219
.2258

.2178
.2217

•9

oo *o

.4092

.4044
.4088

.1

1.0637

1 .0601

.6

.2298

.2256

• i

•4' ; >

.2

i .0671

1.0635

.7

•2337

.2295

.2

-4226

•3

i .0706

I -0670

.8

•2376

•2334

•3

.4270

.4

1.0741

I .0704

•9

.2416

•2374

•4

.4266

1.0776

I .0739

86.0

•24'3

.5

.4360

.6

i .081 1

I .0774

.1

.6

.4405

.7

i .0846

1 .0809

.2

•2535

•2493

.7

.4401

•9
82.0

1.0881
1.0917

'•^

i .0844 !

i .oSSo
1.0915

•3
•4

•9
91 -o

.4496
.4586

•449'

.1

i .0988

1.0950

.6

.2696

•2653

•i

.4582

.2

i .1024

1 .0986

.2693

I. 10^

I .1022

•3

•4

1.1095

1.1057

•9

.2818

•2774

•4

.4770

.4720

1.1169

1.1093

87 .0
.1

.2900

.2815

.4*62

•7

i .1203

I .1 165

.2

•7

.4909

.4858

268

TABLE II.

[BOOK i.

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at
Equator,

Force in Inches of
Merc, at 32°, at
Sea Level at Dub-
lin (Lat 53C 2i>

Tempe-
rature.

Force in Inches of
Mercury at 32 ,
at Sea Level at

K<|iiator.

Force in Inches of
Merc, at 32 , at
Sea Level at Dub-
lin (Lat. 53° 21').

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at
Eqnator.

Force in Inches of
Merc, at 32 , at
Sea Level at Dub-
lin (Lat 53° 21').

9i°.8

H955

'.4904

94°.6

^63 I I

'.6256

97°-4

'•7773

'.7712

•9

.5002

.4951

•7

.6362

.6306

•5

.7827

.7767

92 -o

.5049

.4998

.8

.6412

.6356

.6

.7882

.7821

.1

.5096

.5044

•9

.6463

.6407

•7

•7936

•7875

• 2

•5'43

.5091

95 -°

.6514

.6457

.8

•799 1

•793°

•3

.5190

•5'38

.1

.6564

.6508

•9

.8046

.7984

•4

•5237

.5185

.2

.6615

.6559

98 .0

.8101

.8039

•5

.5285

•5233

•3

.6667

.6610

.1

.8156

.8094

.6

•5332

.5280

•4

.6718

.6661

.2

.8211

.8149

•7

.5380

.5328

•5

.6769

.6712

•3

.8266

.8204

.8

.5428

•5375

.6

.6821

.6764

•4

.8322

.8260

•9

.5476

•5423

•7

.6873

.6815

•5

.8378

.8315

93-o

.5524

•5471

.8

.6924

.6867

.6

•8434

•8371

•5572

•55'9

•9

.6976

.6919

•7

.8490

.8427

.2

.5621

•5567

96 .0

.7029

.6971

•8

.8546

.8482

•3

.5669

.5616

.1

.7081

.7023

•9

.8602

.8539

•4

.5718

.5664

.2

•7'33

.7075

99 <0

.8658

•8595

•5

.5766

•57J3

•3

.7186

.7127

.1

.8715

.8651

.6

.5815

.5761

•4

-7238

.7180

.2

.8772

.8708

•7

.5864

.5810

•5

.7291

.7232

•3

.8829

.8764

.8

•59'3

.5859

.6

•7344

.7285

•4

.8886

.8821

•9

-5963

.5908

•7

•7397

•7338

•5

•8943

.8878

94 -o

.6012

.5958

.8

•745 '

•7391

.6

.9000

.8935

.1

.6062

.6007

•9

.7504

•7445

•7

.9058

.8993

.2

.61 1 1

.6056

97 -°

•7558

.7498

.8

.9115

.9050

•3

.6161

.6106

.761 1

•7551

•9

•9*73

i .9108

•4

.6211

.61561

.2

.7665

.7605

•5

.6261

.6206 j

•3

.7719

.7659

CHAP. II.]

ELASTIC FORCE OF AQUEOUS VAPOUR.

269

TABLE III.

TABLE of the elastic Force of aqueous Vapour from 185° to 214° F.
for every tenth of a Degree.

Tempe-
rature.

Force in Inehesof

at Sea Level at
tor,

i Force iii lip
M. n . ,n
Sea Level at Dub-
lin (Lat. 53' 21').

Tempe-
rature.

Force in liirln-i.f
.M> ivury at 32",
- a Level at
Equator.

Force in Im-ln- ..!'
Merc, at 32°, at
SeaLevelat Ihil.-
lin(Lat. 53' 21')

Tempe-
rature.

!P|

Force in Inches of
Merc, at 32°, at
SeaLevelat Dub-
lin (Lat 53° 21').

i85°.o

17^093

17^034 i88°.6

i8(.48i

I 8^41 8

I92°.2

i 9^062

1^.894

.1

17.130

17.072

•7

18.521

18.458

•3

20.005

'9-937

.2

17.167

17.109

.8

18.561

18.498

•4

20.048

19.979

•3

17.205

17.146

•9

18.601

18.537

•5

20.090

20 .022

•4

17.242

17.184

189 .0

18.641

18.577

.6

20-'33

20 .064

•5

17.280

17.221

.1

18.681

18 .617

•7

20.176

20.107

.6

17.318

17.259

.2

18.721

18.657

.8

20.219

20.150

.7

'7-356

17.296

•3

18.762

18.698

•9

20.262

20.193

.8

'7-393

'7-334

•4

18.802

18.738

'93 -°

20.305

20.236

«9

'7-43'

17.372

•5

18.842

18.778

20.348

20.279

186 .0

17.469

17.410

.6

18.883

18.819

.2

20.391

20.322

.1

17.507

17 .44s .7

18.924

18.859

•3

20.365

.2

'7-545

17.486

.8

1 8 .964

1 8 .900

•4

20.478

20.408

•3

.4

17.622

17.524
17.562

•9

190 .0

19.005
1 9 .046

1 8 .940
18.981

:i

20.521
20.565

20.451
20.49,-

•5

17.660

17.600

.1

19.087

19.022

•7

20.608

20,538

.6

17-638

.2

19.128

19.062

.8

20.652

20 582

•7

'7-737

17.677

•3

19.169

19.103

•9

20.696

20-625

.8

'7-775

17*715

-4

19.210

19.144

194.0

20.740

20 .669

•9

17.814

'7-753

•5

19.251

19.185

.1

20.783

20.713

187 .0

'7.853

17.792

19.292

19.226

.2

20.827

.1

17.891

17.830

.7

'9-334

19.268

20.871

20.800

.2

17.930

17.869

'9-375

19.309

•4

20.916

20 .844

•3

17.908

•9

19.416

'9.350

20 .960

20.888

•4

18.008

'7-947

191 .0

19.458

19.392

2 I .004

20.932

•5

18.047

17.986

.1

19.500

'9-433

•7

21 .049

20.977

.6

•7

18.086
18.125

18.025
18.064

.2

•3

19.583

10 475
19.516

.8
•9

21 .093

•- ' •! 37

21 .021
21 .065

.8

I 8 . i 65

18.103

•4

19.625

195.0

21 .182

21 .1 10

18.204

•5

19.667

19.600

188 .0

18.181 I

.6

19.709

19.642

.2

21.199

.1

•7

19.684

•3

.2

18*260

.8

'9-793

19.726

•4

21 .361

21 .288

•3

•4

I 8 .401

•9

192 .0

19.835
19.878

19.768
19.810

i

2 1 .406

21 -333
21.378

•5

•'

,

19.920

19.852

270

TABLE III.

[BOOK i.

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at
Equator.

Force in Inches of
Merc, at 32°, at
Sea Level at Dub-
lin (Lat. 53° 21').

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at
Equator.

Force in Inches of
Merc, at 32', at
Sea Level at Dub-
lin (Lat. 53 5 21').

Tempe-
rature.

Force in Inches of
Mercury at 32°,
at Sea Level at
Equator.

Force in Inches of
Merc, at 32°, at
Sea Level at Dub-
lin (Lat. 53° 21').

i95°.8

21^542

2I{.468

200°.3

23i.66l

23i.58i

204°. 8

25i-952

25^863

•9

21.587

21.513

•4

23.710

23.629

•9

26.005

25.916

196 .0

21 .632

21.559

•5

23.759

23.678

205 .O

26.058

25.969

.1

21.678

2 I .604

.6

23.808

23.727

.1

26.111

26.022

.2

21 .723

2 I .649

•7

23-858

23.776

.2

26.164

26.075

•3

21.769

21.695

.8

23 -9°7

23 .826

•3

26.217

26.128

•4

21 .815

21.740

•9

23.956

23-875

•4

26.271

26.181

•5

21 .86l

21 .786

2OI .0

24 .006

23.924

•5

26.324

26.234

.6

21.907

21 .832

.1

24.056

23.974

.6

26.378

26.288

•7

21-953

21.878

.2

24.105

24.023

•7

26.431

26.341

.8

21 .998

21.923

•3

24.155

24.073

.8

26.485

26.395

•9

22 .045

21.969

•4

24.205

24.122

•9

26.539

26.449

197 .0

22 .091

22.015

•5

24.255

24.172

206 .0

26.593

26 .502

.1

22.137

22.062

.6

24.305

24.222

.1

26.647

26.556

.2

22.183

22 .108

•7

24-355

24.272

.2

26.701

26 .610

•3

22.23O

22.154

.8

24.405

24.322

•3

26.755

26 .664

•4

22 .276

22 .200

-9

24-455

24-372

•4

26.810

26.718

•5

22.323

22.247

202 .0

24.506

24.422

•5

26.864

26.772

.6

22.370

22.293

.1

24.556

24473

.6

26.918

26.827

•7

22 .416

22.340

.2

24.607

24.523

•7

26.973

26.881

.8

22.463

22.387

•3

24.657

24-573

.8

27 .028

26.936

•9

22.5IO

22.433

•4

24.708

24.624

•9

27.082

26.990

198 .0

22.557

22 .480

•5

24.759

24.675

207 .0

27-'37

27.045

.1

22 .604

22.527

.6

24.810

24.725

'i

27.192

27 .100

.2

22 .651

22.574

-7

24.861

24.776

.2

27.247

27.154

•3

22.699

22 .621

.8

24.912

24.827

•3

27.302

27.209

•4

22.746

22.668

•9

24.963

24.878

•4

27.358

27.264

•5

22.793

22 .716

203 .0

25.014

24-929

•5

27.413

27.319

.6

22.841

22.763

.1

25 .066

24.980

.6

27.468

27.374

•7

22.889

22 .8ll

.2

25.117

25.031

-7

27.524

27-430

.8

22.936

22.858

•3

25.169

25.083

.8

27.579

27.485

•9

22 .984

22.906

•4

25 .220

25.*34

•9

27.635

27.541

199.0

23.032

22.953

•5

25.272

25.186

208 -o

27.691

27.596

.1

23 .080

23 .OOI

.6

25-324

25.237

.1

27.747

27.652

.2

23.128

23 .049

•7

25-376

25.289

.2

27.803

27.708

•3

23.176

23.097

.8

25.428

25- 341

•3

27.859

27.764

•4

23.224

23.H5

•9

25.480

25.393

•4

27.915

27 .820

•5

23.272

23.193

204 .0

25-532

25.445

•5

27.971

27.876

.6

23.320

23.241

.1

25.584

25.497

.6

28.027

27.932

•7

23.369

23.289

.2

25.636

25.549

-7

28.084

27.988

.8

23-4I7

23.338

•3

25.689

25 .601

.8

28.140

28.044

•9

23 .466

23.386

'4

25.741

25.653

•9

28.197

28.101

200 .0

23-5J5

23.435

'5

25-794

25.706

209 -o

28.254

28.157

.1

23-563

23.483

.6

25 .846

25.758

.1

28.311

28.214

.2

23 .612

23.532

-7

25.899

25.811

.2

28.367

28.271

CHAP. II.]

ELASTIC FORCE OF AQUEOUS VAPOUR.

271

"3 -' **

"5 - .er*

*= --

*c -g £ f^

"5 ~~

*o +> J>s^

Tempe-

aj °« *

Tempe-

|M?

Tempe-

B • • «l

L ]l ~'

rature.

8 11 3

rature.

= t'rt ^

11 J«

| g 1 3

rature.

fW

ij i =

Is*

£SJI'

ll«

!*il§

209°.3

28H24

28i.328

2IOC.9

2^.350

2^.250

2i2°-5

30^300

30*. 1 96

•4

28.482 28.385

21 I .0 29.408

29.308

.6

30.360

30.256

•5

28.539 28.441

.1

29.467

29-367

•7

30.420

30.316

.6

28 .596 j 28 .499

.2

29.526

29.425

.8

30 .480

30.377

'.8
•9

28.653
28.7H
28.768

28.556

28.613
28.670

-3
•4

29.585
29.644

29 -7°3

29 .484

29-543
29 .602

•9
213 .0
.1

30.541

30.602
30.662

30-437

30 497
30.558

2IO .O

28.826

28.728

.6

29.762

29 .661

.2

30.723

30.618

.1

28.884

28.786

•7

29 .821

29.720

•3

30.784

30.679

.2

28.942

28 .843

.8

29.881

29.779

-4

30.845

30.740

•3

29 .000

28 .901

.9

29 940

29.838

• 5

30.906 30.801

•4

29.058

28.959

212 .0

30 .000

29.898

.6

30.967 30.861

• 5

29.1 16

29.017

.1

30.060

29.957

•7

31 .029

30.923

.6

29.174

29.075

.2

30.120

30.017

.8

31.090

30.984

•7

29.233

29-'33

'3

30.179

30.076

•9

31.152

31.045

.8

29.291

29.191

•4

30.239

30.136

272

TABLE IV.

[BOOK i.

TABLE IV.

TABLE of the Values of (i + n sin2 X) and its Reciprocal for every
5° of Latitude.

\.

(i+nsin'X).

Log (i + nsin2\).

,

T.AO- I I

i + n sin8 X *

^ViTTdrfx/

f

I .OOO 040

o.ooo 017 52

0.999 959

1.999 982 48

IO

i.ooo 1 60

o.ooo 069 57

0.999 84°

1-999 93° 43

15

i. ooo 356

o.ooo 15455

0.999 644

1-999 845 45

20

i.ooo 622

o.ooo 269 84

0.999379

1-999 73°' 6

25

i.ooo 949

0.000411 94

0.999 °52

1.999 588 06

3°

i.ooi 328

o.ooo 576 49

0.998 674

l-999423 51

35

i. oo i 748

o.ooo 758 48

0.998 255

1-999 241 52

40

1.002 195

o.ooo 952 36

0.997 8°9

1.99904764

45

I.OO2 657

O.OOI 152 22

0.997 35°

£.998 847 78

5°

1.003 118

o.ooi 351 99

0.996 892

1.998 648 01

55

1.003 565

0.001 545 60

0.996 447

£.998 454 40

60

1.003 985

o.ooi 727 18

0.996 031

1.998 272 82

65

1.004 364

o.ooi 891 24

0.995 655

1.998 108 76

70

1.004 692

O.O02 032 8O

o-995 330

7.997 967 20

75

1.004957

O.OO2 147 60

0.995 °67

1-997 852 40

80

1.005 153

0.002 232 17

0.994 874

1-997 767 83

85

1.005 273

0.002 283 95

0.994755

1-997 7 16°5

90

1.005 313

O.002 3OI 38

0.994715

1.997 698 78

HAP. II.]

ABSOLUTE DILATATION OF MERCURY.

273

TABLE V.

TABLE of the absolute Dilatation of Mercury from 32° to 652° F.

Tempe-
rature.

T.

Dilatation from 32°
to T°.

ST.

Mean Coefficient of
Dilatation for i°,
from 32 to T .
S.

Tempe-
rature.

T.

Dilatation from 32°
to T°.

ST.

Mean Coefficient of
Dilatation for i°,
from 32° to T°.
$.

32°

0.000 000 000

o.ooo ooo ooo

352°

0.032 617 314

o.ooo ioi 929

11

o.ooi 991 866

O.OO2 790 358

o.ooo 099 593
o.ooo 099 656

37*
392

0.034 708 842

0.036 806 595

o.ooo 1 02 085
o.ooo 1 02 241

72

0.003 989 962

o.ooo 099 749

412

0.038 910 581

o.ooo 1 02 396

92

0.005 994 286

o.ooo 099 905

432

0.041 020 790

o.ooo 1 02 552

112

0.008 004 840

o.ooo 100 060

452

0.043 '37 232

o.ooo 1 02 708

I32

o.oio 021 623

o.ooo 100 216

472

0.045 259 9°6

O.OOO I O2 863

152

O.OI2 044634

o.ooo 100 372

492

0.047 3^8 798

o.ooo 103 019

172

0.014073 872

o.ooo ioo 528

512

0.049523932

o.ooo 103 175

I92

0.016 109 338

o.ooo ioo 683

532

0.051 665 280

o.ooo 103 331

212

0.018 151 034

o.ooo ioo 839

552

0.053 812 872

o.ooo 103 486

232

O.O2O 198 960

o.ooo ioo 995

572

0.055 966 685

o.ooo 103 642

2$2

0.022 253 114

o.ooo 101 151

592

0.058 126 727

o.ooo 103 798

272

o 024 313 500

o.ooo 101 306

612

0.060 292 990

o.ooo 103 953

292

0.026 380 1 1 1

o.ooo ioi 462

632

0.062 465 492

o.ooo 104 109

3'2

0.028 452 951

o.ooo ioi 618

652

0.064644 221

o.ooo 104 265

332

0.030 532017

o.ooo ioi 773

274

TABLE VI.

[BOOK i.

TABLE VI.

TABLE of the Expansion of Flint and Crown Glass from 32° to

652° F.

FLINT GLASS.

CROWN GLASS.

FLINT GLASS.

CROWN GLASS.

Tempe-
rature.

Mean Coefficient of

Mean Coefficient of ;

Tempe-
rature.

Mean Coefficient of

Mean Coefficient of

T.

Expansion for i°,

Expansion for i°,

T.

Expansion for i°,

Expansion for i°,

from 32° to T°.

from 32° to T°.

from 32° to T°.

from 32° to T°.

3*°

O.OOO OOO OOO

O.OOO OOO OOO

352°

O.OOO OI 2 790

o.ooo 015 975

52

0.000012 571

o.ooo 014 608

372

O.OOO OI2 804

o.ooo 016 066

72

O.OOO OI2 585

o.ooo 014 699

392

O.OOO OI2 819

o.ooo 016 157

92

O.OOO OI2 60O

o.ooo 014 790

412

O.OOO OI2 833

o.ooo 016 248

112

O.OOO OI 2 614

o.ooo 014 88 1

432

O.OOO 012 848

o.ooo 016 339

I32

O.OOO 012 629

o.ooo 014 972

452

O.OOO OI2 863

o.ooo 016430

I52

O.OOO O I 2 644

o.ooo o 1 5 064

472

O.OOO OI2 877

o.ooo 016 521

I72

O.OOO OI2 658

o.ooo 015 155

492

0.000 OI2 892

o.ooo 016 612

I92

O.OOO OI2 672

o.ooo 015 246

512

O.OOO OI 2 906

0.000016 703

212

O.OOO OI2 687

o.ooo 015 337

532

O.OOO OI2 921

o.ooo 016 795

232

0.000012 702

o.ooo 015 428

552

O.OOO OI2 936

o.ooo 016 886

2S2

O.OOO OI2 717

o.ooo 015 519

572

O.OOO 012 950

o.ooo 016 977

272

O.OOO OI2 731

o.ooo 015 610

592

O.OOO OI2 965

o.ooo 017 068

292

O.OOO OI2 746

o.ooo 015 701

612

O.OOO OI2 980

o.ooo 017 159

3I2

O.OOOOI2 760

0.000015 792

632

o.ooo o 1 2 994

o.ooo 017 250

332

0.000012 775

0.000015 883

652

0.000013 009

0.000017 341

CHAP. II.] INDICATIONS OF AIR THERMOMETER.

275

TABLE VII.

Comparison of the Indications of an Air TJiermometer, corrected for
the Expansion of its Envelope, icit/i tfwse of Mercurial Thermo-
meters in different Envelopes.

Tempera-
ture as given

l.yAirThrr-
mometer.
(7-.)

Temperature given by Mercurial Thermometer.

Flint Glass.

(0

Crown Glass.
(<•)

Green Glass.
(*>)

Swedish Glass.
(<•>

212°

2I2°.00

2I2°.00

2 I 2°.00

2 I 2°.00

230

230 .09

229 .96

230 .05

230 .04

248

248 .22

247 .91

248 .14

248 .07

266

266 .36

265 .84

266 .25

266 .13

284

284.52

283 -73

284 .38

284 .20

302

302 .72

301 .64

302 .54

302 .27

320

320 .92

3^9-53

320.72

320.36

338

339 -'7

337 -42

338 .90

338 -47

356

357 -44

355 -33

357 -°8

356-59

374

375 -82

373 -37

375 -26

374 -74

392

3941-25

39 1 -46

393 -44

392 -90

410

412 .75

409.55

411 .80

41 1 .10

428

431 .28

427 .64

430.16

429-35

446

449 -89

445 -73

448.56

447 .62

464

468 .59

463 .82

466 .88

466 .09

482

487 .40

482 .09

485 -33

484 .59

500

506 .19

500 .36

503 .87

518

525 .02

518 .68

522 .50

536

544.06

S36 -94

541 -'3

554

563.18

555 -44

559 -94

57*

582 .30

573 -94

590
608

60 I .6l
621 .05

592.61
61 1 .24

626

640 .80

630.32

644

660 .74

649 .40

662

680 .90

669 .20

TABLE VIII.

[BOOK i.

TABLE VIII.

TABLE of the Density ofvarioits Gases and Vapours, as determined
by Experiment, the Density of Air being i.ooo.*

SIMPLE BODIES.

Name of Substance.

Volume of Vapour
corresponding to
chemical Equiva-
lent.

Symbol.

Density.

Obser-
ver.

Hydrogen,

I

»>
I

»?
»»

i

M

I

»

i

»
I

1

~5

»>

2
I

*

H.

»»
C.

N.

M

0.

»»

Cl.

»»

»>

p.

»»

Br.

S.

M

?•

As.

0.0688
0.06926
0.4145
0.9720
0.97137
I.IO26
1.10563

2-395
2.424
2.470
4.420
4.580
£540

6-5635
6.9
6.976
8.716
10.6

BO.&D.

Reg.
Reg.
Bo.&D.
Reg.
Bo.&D.
Reg.
H.Da.
G.
G.&T.
D.
M.
M.
D.
M.
D.
D.
M.

Ditto,

Carbon (hypothetical), . .

Ditto,

Ditto,

Ditto,

Ditto,

Phosphorus,

Ditto,

Bromine,

Sulphur,

Ditto,

BINARY COMPOUNDS.

Name of Substance.

Composition by Volume.

Density.

Obser-
ver.

Light carburetted hydrogen,
Ammoniacal Gas, . . .
Water,

2H+iC = H,C.
iN+3H = 2NH3.
2H+iO = 2HO.

»> 11

°-5555

0.5901
0.6235
0.6250

Th.
H.Da.
G. L.
Dz.

Ditto,

* For a complete list of all the gases and va-
pours whose densities had been examined up to
the year 1840, see Poggendorff's Annalen,

torn. xlix. p. 417 (i 840), and Dove's Reperto-
riumder Physik, vii. p. 174.

CHAP. II.] DENSITY OF VARIOUS GASES AND VAPOURS.

277

Name of Substance.

Composition by Volume.

Density.

Obser-
ver.

Carbonic oxide, ....

2C+IO + 2CO.

iH + aC-H,Q»

iN+iO = 2NO,.
iP + 6H = 4PH,.

6H+iS = 6HS.
ill-f iCl = 2HCl.
i> »»
iC+ iO = C02.

2N+iO='2NO.

iN + 2C = NGi.
iS + 6O = 6SO2.

iB + 3F=2BF3.

»> »»
iAs + 6H = 4AsH3.
iS + 9O = 6SO3.

iSi + 2F = SiF2.

iB + 3Cl = 2BC13.
iH+iI = 2HI.
iP + 6Cl = 4PCl3.
iSi-»-2Cl = SiCl2.
iAs + 6Cl = AsC!3.
iTi + 2d = TiCl2.
iSn + 2Cl = SnC!2.
ilL id HgCl.
illg+ iBr- IL'l'.r.
iAs + 3O = AsO3.
iHg+il Ugl.
i As + 61 = 4AsI,.

ERNARY COMPOUNDS.

ill • iN + 2C = 2lINC,.
8C + 1 2 11 + 20 = 4C4H6O,.
4C^4H^4O = 4CaH3O4.
8C + 8H + 4O-4C4HtO4.
8C+ioH + O = 2CJl 0,
i6C+i6II 4() 4C 1LO4. '
40C • .' :!l 10 +C II.jOj.
SC-noH + I- 2( .11 1.

0.9678
0.9709
.0388
.1214
.146
.1912
.2474
.278

•5245
.52901
.5204
.8064
2.193

2-2553
2.3124

2.3709
2.695
3.000
3.600

3-5735
3-942

4-443
4-875

5-9390
6.3006
6.836
9.1997
9.8
12. 16
13.85
15.9
16.1

0.9476
'33

2.08
2.586

3-07

5-4749

Th.
Br.
D.
Ro.

B.&A.
G.
Bo.&D.

8*

G.
11. Da.
G.&T.
D.
J. Da.
D.
M.
D.
J. Da.
D.
G.
D.
D.
D.
D.
D.
M.
M.
M.
M.
M.

G.

Ca.
G.
Ca.

G.»

Binoxide of nitrogen, . .
Phosphuretted hydrogen, .
Ditto

Hydrosulphuric acid, . .
Hydrochloric acid, . . .
Ditto, ... .

Carbonic acid, ....
Ditto .... .

Protoxide of nitrogen, . .

Sulphurous acid, ....
Ditto .

Fluoboric acid, ....
Ditto,

Arseniuretted hydrogen, .
Sulphuric acid, ....

Fluosilicic acid, ....
Ditto

Terchloride of boron, . .
Hydriodic acid, ....
Terchloride of phosphorus,
Chloride of silicium,
Terchloride of arsenic, . .
• loride of titanium, . .
iloride of tin, ....
Chloride of mercury, . .
Bromide of mercury, . .

•••„ . . .
Iodide of arsenic, ....

T

Hydrocyanic acid, . . .

1 6° C.), .
;ic acid (at 250° C
Sulphur. . .
Butyric acid (at 261° C.), •
;t 338°C.),
Hydnn.lir rthcr, ....

'•/ nation nfContrac tiont— Tli . .
Ur.. P.. :.-. !:-.. : C. fc T., Gay-Lumac ami
Tlu-nanl ; 1!.\ A.. Ili.-t nnd Ar.ip.; (i., G«y-
Lussac ; Do. & D., Boussingault and Dumas ;

.. .: ('., C.-lin: II. Pa., Sir Hum-
phrey Davy; D., Duma.-.; ,T. P.i.. Dr. John
Mitocherlich; Dx., Deapretz; I»in..
Dineau ; Ca., Cahoan ; Ro., Rote.

TABLE IX.

[BOOK i.

TABLE IX.

TABLE oftfie Weight o/ioo cubic Inches of Air, Hydrogen, Nitro-
gen, Oxygen, and Carbonic Acid Gas.

Name of Gas.

Density.

Weight at 3 2° F.t and
under the Pressure of
30 Inches of Mercury
at the Equator.

Weight at 3 2° F., and
under the Pressure of
30 Inches of Mercury
at Dublin.

Air,

1. 00000

0.06926
0.97137
1.10563
1.52901

32^.690 541
2 .264 147
31 .754611
36 .143643

49 .984 164

32*rs.8o2 342

2 .271 890
31 .863 211
36 .267 253

.5° -'55 '09

Hydrogen, ....
Nitrogen, ....

Carbonic acid, . . .

TABLE X.

TABLE of the elastic Force of the Vapours of Alcohol, Ether, Oil of
Turpentine, Petroleum or Naphtha, and Sulphuret of Carbon,
at different Temperatures, expressed in Inches of Mercury.

Ether.
(URK.)

Alcohol,
Sp. gr. 0.813.
(URE.)

Alcohol.
Sp. gr. 0.813.

(URE.)

Petroleum.

(URE.)

Sulphuret of
Carbon.*
(MARX.)

Temp.

Force of
Vapour.

Temp.

Force of
Vapour.

Temp.

Force of
Vapour.

Temp.

Force of
Vapour.

Temp.

Elastic
Force.

34

6.2O

32

0.40

i93°-3

46.60

3i6°

30.00

•7°

3^487

44

8.10

40

0.56

196.3

50.10

320

3I-7°

22

3-963

ft

10.30
13.00

45
5°

0.70
0.86

200
206

53-oo
60. 10

325
330

34.00
36.40

27

32

4-493
5 .082

74

16.10

55

1. 00

210

65.00

335

38.90

37

5-733

84

20.00

60

1.23

214

69.30

340

41.60

42

6 -453

94

24.70

65

1.49

216

72.20

345

44.10

47

7.246

* Dove's Repertorium der Physik, i. p. 54.
This table has been calculated by means of the
formula,

in which i represents the elastic force in inches of
mercury, and T the temperature in Fahrenheit
degrees, counted from 32°.

CHAP. II.]

ELASTIC FORCE OF VARIOUS VAPOURS.

279

Ether.
(URE.)

Alcohol,
Sp. gr. 0.813.

UK.)

Alcohol,
Sp. gr. 0.813.

(URE.)

Petroleum.

(URK.)

Sulphuret of
Carbon.
(MARX.)

Temp.

Force of
Vapour.

Temp.

Force of
Vapour.

Temp.

Force of
Vapour.

Temp.

Force of
Vapour.

Temp.

Elastic
Force.

104

30.00

70

..76

220°

78.50

350°

46.86

52°

S'.l^

105

30.00

2.10

225

87.50

3I5

50.20

57

9.077

I 10

32.54

80

2.45

230

94.10

360

53-3°

62

10.127

H5

35-90

85

2.93

232

97.10'

365

56.90

67

II .276

1 20

39-47

90

3-40

236

103.60

37°

60.70

72

12.531

125

43-24

95

3-9°

238

106.90

372

61.90

77

13.898

130

47-!4

IOO

4.50

240

I ll.24|

i Y Q i r\

375

64.00

82

15.385

!35

51.90

105

5-20

244

I I O.ZO

7

1 7 .001

140
H5

56.90
62.10

I 10

115

6.00
7-io

247
248

122. IO |
126.10

Oil of Turpentine.
(URE.)

92

97

18.754
20 .651

15°

67.60

120

8.10

249.7

131.40

Force of

IO2

22 .703

155

73.60

125

925

250

132.30 j

Temp.

Vapour.

I07

24.918

1 60

80.30

I30

1 0.60

252

138.60

I 12

27 -306

165

86.40

12.15

254-3

143-7°!

304°

30.00

I 17

29.876

170

92.80

I40

13-9°

258.6

151.60 ;

307.6

32.60

122

32 .640

'75

99.10

H5

260

155.20

310

33-5°

127

35.607

1 80

108.30

150

18.00

262

161.40

3i5

35.20

132

38.788

185
190

1 1 6. 10
124.80

I 60

20.30
22.60

264

1 66. 10

320
322

37.06
37.80

137
I42

42.194

45 -838

195

133-70

,65

25.40

326

40.20

200

142.80

170

28.30

33°

42.10

205
210

151.30
166.00

"73

178.3

30.00
33-5°

336

34°

45.00
47-3°

1 80

34-73

343

49.40

182.3

36.40

347

51.70

185.3

39-90

35°

53.80

190

43.20

354

56.60

362

62.40

280

SUPPLEMENT TO TABLE X.

[BOOK i.

SUPPLEMENT TO TABLE X.

Elastic Force of Vapours generated in a very limited Space, accord-
ing to M. Cagniard De la Tour*

Ether (Series I.)t

Ether (Series II.)J

Sulphuret of Carbon. §

Temp.
(Centigr.)

Force in At-
mospheres.

Temp.
(Centigr.)

Force in At-
mospheres.

Temp.
(Centigr.)

Force in At-
mospheres.

80°

5.6

80

4.2

90

7-9

....

....

90

5-5

IOO

10.6

IOO

14.0

IOO

7-9

no

12.9

no

17-5

110

10

120

1 8.0

I2O

22.5

120

13

130

22.2

130

28.5

130

i6.5

140

28.3

140

35

140

2O.2

150

1 60
170
1 80

37-5
48.5

59-7
68.8

T

1 60

170
180

42
50.5

I50

1 60
170
1 80

24.2

28.8
33-6
4O.2

190

78.0

190

66

190

2OO

47-5

T7.2

200

86.3

200

70.5

2IO

j i

66.c

210

92-3

210

74

J

220

104.1

220

78

220

77.8

230

112.7

230

81

230

89.2

240

119.4

240

85

240

98.9

250

123.7

250

89

250

1 14.3

260

130.9

260

94

260

129.6

* Ann. de Chim. et de Phys., tome xxii.
p. 411.

f In this series the liquid originally oc-
cupied seven parts of the tube. When to-
tally converted into vapour it filled twenty.

% In this case the liquid occupied three

and a half parts, the vapour, as before,
twenty; in both cases the liquid passed
completely into the vaporous state at 150°.
§ The liquid occupied eight parts, the
vapour twenty. The transition to the state
of vapour took place at 220°.

ADDENDA.

Page 104. — Add the following note to (68):

Not long after the passing of the Act of 1824 the fire which
destroyed the houses of Parliament so far injured the legal stan-
dards as to render their restoration necessary, and a Commit t« <
was accordingly appointed in 1838 to consider the best means
of effecting this object. This Committee reported* in 1841,
that subsequent to the passing of the Act of 1824 it had been
discovered that several elements of the reduction of pendulum -
experiments, therein referred to, were doubtful or erroneous;
and similarly, that the determination of the weight of a (
inch of distilled water is also attended with considerable u:
tainty. They were, therefore, of opinion that the method of
restoring lost standards, recommended by the Act of 1824, could

• 1 on, and expressed th«'m*«'lve$ "fully persr.
that, with reasonable precautions, it will always be possil
provide for the accurate restoration of the standards, by in
of material cojiir.-t which have been carefully compared with them,
more securely than by \perimen:

iral constants." In th avaih.lt

selves, for the restoration of the standards, o!
nomical Society's scale, the Royal Society's scale, the iron bars
belonging to the Board of Ordnance, and several met all;
which had been most accurately compared with their re^j ,
standards.

157, last paragraph — On the same principle M. Pi.-uiL-:;;.

plar • .arkiible tact, which In-ha* r-

that the human body may be brought with impunity intu c< :

irliaraenUry Papers, 1842, vol. xxv. p. 263.
2 0

282 ADDENDA. [BOOK I-

with metals in a state effusion, and at very high temperatures.
Thus the naked hand may be passed through a stream of mol-
ten metal, or plunged into a bath of the same ; it appears only
necessary that the skin should be in its normal healthy, moist
state, and that the operation should not be performed too ra-
pidly. M. Boutigny supposes that the natural moisture of the
skin assumes the spheroidal state, that accordingly there is no
actual contact between it and the metal, and that the heat ra-
diated by the latter is reflected from the surface of the moisture
enveloping the skin. Of course if the skin were exposed to the
action of the heat until all the moisture was evaporated, it would
be no longer thus protected.

Page 194. — It is to be observed that the volume Vt of the glass bal-
loon at the temperature t of the surrounding medium may also
be obtained by the method of gauging with mercury, and its vo-
lume at the temperature of melting ice obtained from the former^
by means of the known expansion of the glass of the balloon and
of the gauging vessel.

219. — This hypothesis of an imperfect vaporization, and of an

intermediate or transition state between the liquid state and that
of vapour, appears to derive confirmation from M. Cagniard De
la Tour's experiments on the elastic force of vapours formed in
a very limited space. For on reference to the Supplement to
Table X., p. 280, it will be seen that the rate of increase of
the elastic forces of ether- vapour above 150°, when it is no
longer in contact with its liquid, is so rapid as to be quite in-
consistent with the 'supposition that it is merely due to the
effect of expansion by heat. It will also be seen that this rate
diminishes with the temperature, and that it is much less rapid
in the second series, where the particles of the vapour were less
condensed than in the first. The same remarks apply to the
vapour of sulphuret of carbon.

— 224. — Proposition IV. The probable value and probable error
obtained by means of this proposition should be represented by
the symbols X, It, to distinguish them from those from which
they are derived.

END OF PART I.

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